2) By using standard arguments of the theory of differ- ential equations it can be proved that if T is GUS or GUAS then every trajectory in T is forward complete. Remark 2.2: For non-**switched** time-invariant **systems**, i.e. **systems** of the form x ˙ = f (x), GUAS is equivalent to global asymptotic stability (GAS) that is, GUS plus the global attractiveness of the zero solution (x(t) → 0 as t → ∞ for every solution x). This equivalence is no longer true for families of trajectories of **switched** **systems**. For example, consider the **switched** system in R 2 with two subsystems: f 1 (x) = [x 2 − x 1 ] 0 and f 2 (x) = −x. Let T be the family

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In this work we will consider the different input/output stability properties as well as the IOSS property for **switched** **systems** as in (2) with switchings governed by digraphs. The digraph H ∗ imposes a restriction on the switchings, which results in a family of subclasses of switching signals, so that a switching signal belongs to a certain subclass whenever it takes values in a strongly connected component of H ∗ . The behavior of system (2) when the switchings are restricted to these classes plays a signiﬁcant role, as it will be shown in this work that several uniform stability properties of the system with switchings governed by H ∗ are equivalent to the same properties when the switchings are restricted to each of these

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The paper is organized as follows. In section 2 we establish the notation, and present the basic definitions and main results of the paper. In section 3 we exhibit some examples that show the application of our results to **systems** to which those mentioned above cannot be applied or are of little help. We study the invariance for **switched** **systems** and prove our Invariance Principle in section 4. Section 5 is devoted to the proof of one of the main results. In section 6 we present the conclusions and finally in the Appendix we present some results about compactness of the trajectories of the **switched** **systems** under study. These results, that are used in some proofs along the paper, are also important by their own.

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Abstract—In this paper we study the stability of nonlinear and time-varying **switched** **systems** under restricted switch- ing. We approach the problem by decomposing the sys- tem dynamics into a nominal-like part and a perturbation- like one. Most stability results for perturbed **systems** are based on the use of strong Lyapunov functions, i.e. func- tions of time and state whose total time derivative along the nominal system trajectories is bounded by a negative definite function of the state. However, **switched** **systems** under restricted switching may not admit strong Lyapunov functions, even when asymptotic stability is uniform over the set of switching signals considered. The main contri- bution of the current paper consists in providing stability results that are based on the stability of the nominal-like part of the system and require only a weak Lyapunov func- tion. These results may have wider applicability than results based on strong Lyapunov functions. The results provided follow two lines. First, we give very general global uniform asymptotic stability results under reasonable boundedness conditions on the functions that define the dynamics of the nominal-like and the perturbation-like parts of the system. Second, we provide input-to-state stability (ISS) results for the case when the nominal-like part is **switched** linear-time- varying. We provide two types of ISS results: standard ISS that involves the essential supremum norm of the input and a modified ISS that involves a power-type norm.

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The second chapter is about the robust stability and robust control treated in the context of the **switched** **systems**. For this propose, the stability criteria are exposed along with robust control synthesis based on state feedback and output feedback techniques. The chapter develops a less con- servative LMI robust stability tools using Lyapunov functions that take into account the uncertain parameters. This chapter shows also, the **switched** system representation with uncertainty models, oriented to the stability analysis and control based on linear matrix inequalities. Furthermore, the stability of discrete-time **systems** with time varying delays is analyzed by using a discrete-time ex- tension of the classical Lyapunov-Krasovskii function. Necessary and sufficient LMI conditions for the existence of such functions are presented. Moreover, in this chapter there are examples for the robust control synthesis and for the **switched** **systems** transformation approach are exposed. Chapter 3

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Although the ISS property is important and useful for a wide range of control problems (see Khalil, 2002), it gives no robustness information in the case in which the inputs have bounded power or energy but are unbounded. This fact motivates the introduction of different characteri- zations of robustness (see Angeli and Neˇsi´c, 2001). In this paper we consider the case in which the perturbations are bounded in a novel, compared to previous characterizations, power-like sense. One of the contributions of the paper is to show that the design presented in (Mancilla-Aguilar and Garc´ıa, 2013) semi-globally stabilizes the perturbed **switched** system in a practical sense, and that the stability is robust with respect to small errors in the measurements and to small (in a power-like integral norm) perturbations. Another contribution of the paper is, in the case of **switched** **systems** whose subsystems are homogeneous of degree one, to prove for this controller robust exponential stability results in the case of locally integrable perturbations. It must be pointed out that this general result comprises, among others, the exponential ISS and exponential iISS (integral input- to-state-stability, (see Sontag, 1998)) properties of that design, but gives us a better description of the closed-loop system.

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If the overall system is unstable for a determined bumpless transfer strategy, it is possible that the control signal do not behave as desired and the actuators saturate. The idea is to ﬁnd a bumpless transfer strategy that guaranties the overall system’s stability and that minimizes the discontinuities and bumps on the control signal. Multiple Lyapunov functions are used to ﬁnd the conditions such that the **switched** system is stable under any switching law s, using the closed loop system matrix and evaluating some linear matrices inequalities for all the switching cases available. In this chapter, two theorems about stability for two bumpless transfer strategies and their respective demonstration are presented.

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Abstract—Most of the existing characterizations of the integral input-to-state stability (iISS) property are not valid for time-varying or **switched** **systems** in cases where converse Lyapunov theorems for stability are not available. This paper provides a characteri- zation that is valid for **switched** and time-varying **systems**, and shows that natural extensions of some of the existing character- izations result in only sufficient but not necessary conditions. The results provided also pinpoint suitable iISS gains and relate these to supply functions and bounds on the function defining the system dynamics.

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It is well known that the existence of common or multiple Lyapunov functions suffices to state the (G)UAS of **switched** **systems** under, respectively, arbitrary switchings or restricted ones [1]. Nevertheless, their obtention even for nonswitched **systems** is in general a highly nontrivial task. On the other hand, common or multiple weak Lyapunov functions, i.e., func- tions for which the time derivatives along the trajectories of the subsystems are negative semidefinite, arise rather naturally in many engineering **systems**. In fact, in many cases, the subsys- tems have dissipative models and the energy functions usually constitute common or multiple weak Lyapunov functions. Al- though the existence of weak Lyapunov functions by itself gives no asymptotic stability guarantee, it can be supplemented with other additional conditions in order to yield asymptotic stability. This fact motivated the development of several stability results for **switched** time-invariant **systems** based on weak Lyapunov functions: extensions of LaSalle’s invariance principle [8]–[15] and other approaches [16]–[19]. Most of these papers assume that the switching signals satisfy some dwell-time condition and only provide convergence results.

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In the context of **switched** **systems**, if every switching signal is admissible, then we speak about ‘‘arbitrary switching’’; if switch- ing is constrained to have some minimum dwell-time, we speak about ‘‘dwell-time switching’’. In every case, we may define a set S ⊂ S all containing the admissible switching signals (e.g. all the switching signals under arbitrary switching and only those that have a minimum dwell time under dwell-time switching). By setting Λ = S in (1), it is easy to see that a **switched** system can be identified with a parametrized family of time-varying **systems**, where the admissible switching signals play the role of parameters (i.e. labels). Note that although the index set Γ may be finite, the parameter set Λ is usually infinite since the latter set equals S and not Γ . This is illustrated in the following example. Example 1. Consider the **switched** linear system with two modes and under arbitrary switching, given by

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The contrary is also true, that **switched** **systems** with some of the subsystems unstable can become stable for certain switching signals [14, 6]. From what we have just said it is plain to see that the stability of **switched** **systems** depends on both the dynamics of each subsystem and the switching signals. Intuitively it is easy to imagine a switching signal that maintains stable a **switched** linear system with all its subsystems stable. It is enough to stay for a long time in one of the subsystems and jump into another with a low frequency. This idea, and the mathematical concept of “low frequency of jumping between subsystems”, was developed by Morse and Hespanha with the concepts of dwell time and average dwell time switching [15, 16].

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Health organizations are continually pressured to do more with less, and consequently, the availability of information is essential to decision-making; experience alone can no longer stand as the only basis for choosing a course of action. One of the SAGE/MS major challenges is to implement **systems** and tools in an environment marked by diverse circumstances, **systems** and tools which are capable of unifying information into a single database for the purpose of decision- making and communicating government activity to society. Considering this context, the following research question is presented: How can an information system to provide health information be developed? In other words, the central objective of this research is to illustrate the development of a public health information system in Brazil.

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Gns3: Es un simulador gráfico de red que te permite diseñar topologías de red complejas y poner en marcha simulaciones sobre ellos. Para permitir completar simulaciones, GNS3 está estrechamente vinculada con: Dynamips, un emulador de IOS que permite a los usuarios ejecutar binarios imágenes IOS de Cisco **Systems**.

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Although nowadays code-switching has been widely researched and considered as a common speech style among bilinguals, it was not until 1980 when its linguistic aspects started being studied. Poplack (1980) was the first author who presented an analysis on code-switching in an article whose title mixes both English and Spanish: Sometimes I’ll start a sentence in Spanish y TERMINO EN ESPAÑOL: toward a typology of code- switching. By studying a Puerto Rican community in the United States, she found out that code-switching was a “sensitive indicator of bilingual ability” (Poplack 1980, 616) in opposition to Pedraza (1978) (quoted in Poplack 1980, 583) who believed that speakers code-**switched** due to the lack of command in one of their two languages. Poplack (1980) also studied the constraints which could regulate this phenomenon to a point that she suggested the possibility of a third grammar, a grammar only for code-switching but which consisted on the “overlapping sectors of the grammars of L1 and L2” (615).

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The focus of this study is the type of gender agreement operation that is established in code **switched** agreement structures where English provides the subject and Spanish provides the adjectival subject complement. Bearing in mind the notions presented in section 2.2 on grammatical gender, the hypotheses will mainly deal with two issues: the analogical criterion and the masculine as default agreement. It is argued that these two issues will have a different impact in the various speaker groups, depending on their dominant language or their L1. Therefore, the four hypotheses below capture the predictions for each of the four groups of participants (which will be described in section 4.1. below). They are ordered in terms of the degree of Spanish dominance of the participant groups.

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Of course, the simplest situation corresponds to the case where the family of control **systems** (1.2) is uniformly null controllable (i.e., all its **systems** are null controllable), which is equivalent to say that the family of time-reversed control **systems** (1.4) is uniformly null controllable (see Fabbri et al. [5]). If this is the case, then the set of null controllable points of the system (1.2) coincides with R n for all ω ∈ Ω, and the same happens with the T -reachable sets if the time T is large enough. Therefore, in this paper we will always consider the case of existence of at least one system of the family (1.2) which is not null controllable.

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wild-type behaviour of a selection of 200 circadian genes of the model plant Arabidopsis thaliana. Jenkins et al. showed that their approach allows them to investigate whether genes with similar switch event times also have correlated promoter motifs. Results of both proposal of Sanguinetti et al. and Jenkins et al. support the idea that using a mechanistic model to identify transcriptional switch points is likely to strongly contribute to efforts in elucidating and understanding key biological processes (e.g. transcription and degradation). However, the computational overheads from [1,7] are significant due to complex inference algorithms. It is evident that modelling transcription networks requires the study of a continuous dynamical problem in which the quick time-varying behaviour of the input stimulus can be taken into account. The continuous-time method in [3] using GPs is more appealing, simpler and computationally efficient approach for inference purposes. In 2009, Álvarez et al. introduced a novel hybrid methodology using GPs and differential equations, known as latent force models (LFM). LFM combine data driven modelling with physical models of **systems** [9,10]. Here, the statistical inference of continuous quantities is possible without a discretization process, and it still being computationally efficient. Álvarez et al. [11] also proposed a **switched** dynamical LFM version for the problem of determining robot motor primitives using a second-order ODE, obtaining versatile representation for robot movements that can capture discrete changes and non-linearities in the dynamics.

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Not in all embedded system application is needed to include an operating system, even less common to include a real time operating system, the decision has to do with the complexity of the application, the need of finish an operation before a time constraint, and the available resources to include an operating system, among others. An operating system cannot be included in all types of hardware **systems**, there is a requirement for each operating system in terms of hardware resources. For the project it has been identified the need of real time routines in the acquisition an processing while non real time constraints for system visualization. In the Figure 1, the element blocks of the project system are shown, where the orange blocks represent hard real time software, while blue blocks represent non real time software blocks.

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Abstract: Membrane computing is a recent area that belongs to natural computing. This field works on computational models based on nature's behavior to process the information. Recently, numerous models have been developed and implemented with this purpose. P-**systems** are the structures which have been defined, developed and implemented to simulate the behavior and the evolution of membrane **systems** which we find in nature. What we show in this paper is a new model that deals with encrypted information which provides security the membrane **systems** communication. Moreover we find non deterministic and random applications in nature that are suitable to MEIA **systems**. The inherent parallelism and non determinism make this applications perfect object to implement MEIA **systems**.

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EIGRP: protocolo de enrutamiento de puerta de enlace interior, es un protocolo de encaminamiento de estado de enlace, propiedad de Cisco **Systems** que ofrece lo mejor de los algoritmos de vector de distancias y del estado de enlace. ENRUTAMIENTO: proceso en el que se busca identificar la mejor ruta (ruta más corta) para reenviar paquetes entre redes; teniendo en cuenta diferentes factores como la tabla de enrutamiento, la métrica, la distancia administrativa, el ancho de banda, etc.

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