We propose a novel Lyapunov construction for continuous-time switched systems relying on graph theoretical construction. Starting with finite family of continuously differentiable functions, suitable inequalities involving these functions and the vector fields defining system are encoded in direct labeled graph. then provide sufficient conditions (asymptotic) stability subject to constrained sw...

|Abstract: High-Technological solutions of today are characterized by complex dynamical models. A lot of these models have inherent hybrid/switching structure. Hybrid/switched systems are powerful models for distributed embedded systems design where discrete controls are applied to continuous processes. Hybrid systems are also an important modeling class for nonlinear systems because a wide var...

where { fα(.) : α ∈ Ω}, is a family of functions that is parameterized by some index set Ω, and α(·) ∈ Ω depending on the system state in each time is a switching rule/signal. The set Ω is typically a finite set. Switched systems arise in many practical models in manufacturing, communication networks, automotive engine control, chemical processes, and so on; see for example (D. Liberzon, 2003; ...

The problem of guaranteed cost control is investigated for a class discrete-time saturated switched systems. The purpose to design the law and state feedback such that closed-loop system asymptotically stable upper-bound function minimized. Based on multiple Lyapunov functions approach, some sufficient conditions existence controllers are obtained. Furthermore, conv...

We present a suucient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We als...

This paper focuses on the quadratic stabilization problem for a class of uncertain impulsive switched systems. The uncertainty is assumed to be norm-bounded and enters both the state and the input matrices. Based on the Lyapunov methods, some results on robust stabilization and quadratic stabilization for the impulsive switched system are obtained. A stabilizing state feedback control law reali...

In this paper, the problems of stability for continuous and discrete-time polytopic uncertain switched linear systems with average dwell time switching are investigated. Firstly, the exponential stability result of general continuous-time switched systems using a discontinuous piecewise Lyapunov function approach is revisited, and the discretetime counterpart is then presented by the following ...

This paper is concerned with exponential stability and stabilization of switched linear systems with interval time-varying delays. The time delay is any continuous function belonging to a given interval, in which the lower bound of delay is not restricted to zero. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the...

We present a sufficient condition for asymptotic stability of a switched linear system in terms of the Lie algebra generated by the individual matrices. Namely, if this Lie algebra is solvable, then the switched system is exponentially stable for arbitrary switching. In fact, we show that any family of linear systems satisfying this condition possesses a quadratic common Lyapunov function. We a...

This paper is concerned with the problem of delay-dependent exponential H∞ model reduction for discrete-time switched delay systems under switching signals with average dwell time (ADT). The objective is to construct a reduced-order model, which ensures that the resulting error system under switching signal with ADT is exponentially stable with an H∞ norm bound. A weighting factor α is introduc...