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... right, i.e. x+(t) = lim s↓t x(s). The set of impulsive times I := {tk}k∈N is a countable set of impulse instants tk+1 > tk, k ∈ N and we define the inter-impulse distance as Tk := tk+1 − tk. This quantity is also referred to as dwell-time in the literature. We also assume that the sequence {tk}k∈N has no accumulation point in order to exclude any Zeno behavior. Depending on the structure of the matrices A and J , the system may exhibit very different behaviors. In particular, notions of minimal and maximal dwelltime can be defined for impulsive systems [12], similarly as for switched systems [10, 13]. In the case of impulsive systems, these notions refer to system properties such that too large or too short dwell-times destabilize the system. In the case of periodic impulses with period T > 0, the problem essentially reduces to the study of the Schurness of the matrix JeAT , which turns out to be a very simple problem. However, this formulation suffers from several critical drawbacks: 1. The eigenvalue analysis is not extendable to the case of aperiodic impulses since the spectral radius is, in general, not submultiplicative; 2. To overcome this, Lyapunov approaches can be applied but lea...

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...s is asymptotically stable. Closed-loop and open-loop switching control strategies have been investigated in [22] and [23]. State-feedback and output-feedback switching design have been considered in =-=[27]-=-, [28]. Although these results are nice, they are mainly concerned with deterministic switching, and little effort has been made towards stochastic switching. The selection or determination of stochas...

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...int on the input variable. Switched positive systems, [12], are frequently encountered in many application fields. Examples of switched positive systems are straightforward: networks of tanks regulated by valves opening, chemical plants where reagents concentration can be varied by means of additional inputs, air conditioning systems and TCP congestion control [13]. Despite their ubiquitous nature, a few basic problems, concerning stabilization and performances, still deserve a deeper study. This paper aims at extending results on the stabilization for a continuous-time switched linear system [14], [15] to continuous-time switched linear positive systems of the general form x(t) = Aσ(t)x(t), x(0) = x0, (1) defined for all t ≥ 0, where x(t) ∈ Rn+ is the state variable vector, σ(t) ∈ {1, . . . , N} is the switching signal, x0 ∈ R n + is the initial condition and Ai belongs to the set {A1, . . . , AN}. In order to be a positive system Ai has to be Metzler, i.e. aij ≥ 0, ∀(i, j), i 6= j An innovation with respect to the previous works is the use of the piecewise linear co-positive Lyapunov functions, which are easiest to find and compute. Moreover, we present also a stabilizing switching ...

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...onditions on the bound of the nonlinear part have been derived using the explicit solution of the linear system. However, this scheme cannot be easily extended to the class of switched systems. This paper deals with uncertain switched systems on non-uniform time domains. During the last two decades, many works have investigated this class of systems due to its broad range of applications in various areas [10–12]. Stability and stabilization have been widely studied for switched systems. They can be categorized into two separated directions depending onwhether each subsystem is continuous-time [13,14] or discrete-time [15,16]. Recently, adaptive control laws are proposed to asymptotically track the states of a multimodal piecewise affine reference model in continuous-time [17,18] or discrete-time [19]. ∗ Corresponding author. E-mail addresses: taoussfatima@gmail.com (F.Z. Taousser), michael.defoort@univ-valenciennes.fr (M. Defoort), mohamed.djemai@univ-valenciennes.fr (M. Djemai). http://dx.doi.org/10.1016/j.nahs.2014.12.001 1751-570X/© 2014 Elsevier Ltd. All rights reserved. 14 F.Z. Taousser et al. / Nonlinear Analysis: Hybrid Systems 16 (2015) 13–23 In this paper, the objective is to stu...