A graph theoretic approach to input-to-state stability of switched systems

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS. We allow non-ISS systems in the family and our analysis involves graph-theoretic arguments. A weighted digraph is associated to the switched system, and a switching signal is expressed as an infinite walk on this digraph, both in a natural way. Our class of stabilizing switching signals (infinite walks) is periodic in nature and affords simple algorithmic construction.Comment: 14 pages, 1 figur

Stabilizing switching signals: a transition from point-wise to asymptotic conditions

Characterization of classes of switching signals that ensure stability of switched systems occupies a significant portion of the switched systems literature. This article collects a multitude of stabilizing switching signals under an umbrella framework. We achieve this in two steps: Firstly, given a family of systems, possibly containing unstable dynamics, we propose a new and general class of stabilizing switching signals. Secondly, we demonstrate that prior results based on both point-wise and asymptotic characterizations follow our result. This is the first attempt in the switched systems literature where these switching signals are unified under one banner.Comment: 7 page

Stabilizing Scheduling Policies for Networked Control Systems

This paper deals with the problem of allocating communication resources for Networked Control Systems (NCSs). We consider an NCS consisting of a set of discrete-time LTI plants whose stabilizing feedback loops are closed through a shared communication channel. Due to a limited communication capacity of the channel, not all plants can exchange information with their controllers at any instant of time. We propose a method to find periodic scheduling policies under which global asymptotic stability of each plant in the NCS is preserved. The individual plants are represented as switched systems, and the NCS is expressed as a weighted directed graph. We construct stabilizing scheduling policies by employing cycles on the underlying weighted directed graph of the NCS that satisfy appropriate contractivity conditions. We also discuss algorithmic design of these cycles

Stabilization of discrete-time switched linear systems:Lyapunov-Metzler inequalities versus S-procedure characterizations

\u3cp\u3eIn this paper we study connections between Lyapunov-Metzler inequalities and S-procedure characterizations in the context of stabilizing discrete-time switched linear systems using min-switching strategies. We propose two generalized versions of S-procedure characterization along the lines of the generalized versions of Lyapunov-Metzler inequalities recently proposed in the literature. It is shown that the existence of a solution to the generalized version(s) of Lyapunov-Metzler inequalities is equivalent to the existence of a solution to the generalized version(s) of S-procedure characterization with a restricted choice of the scalar quantities involved in the latter. This recovers some of our earlier works on the classical Lyapunov-Metzler inequalities as a special case. We also highlight and discuss an open question of whether the generalized versions of S-procedure characterization are strictly less conservative than the generalized versions of Lyapunov-Metzler inequalities, which in turn are equivalent to periodic stabilizability as was recently shown.\u3c/p\u3

Stabilization of discrete-time switched linear systems: Lyapunov-Metzler inequalities versus S-procedure characterizations

In this paper we study connections between Lyapunov-Metzler inequalities and S-procedure characterizations in the context of stabilizing discrete-time switched linear systems using min-switching strategies. We propose two generalized versions of S-procedure characterization along the lines of the generalized versions of Lyapunov-Metzler inequalities recently proposed in the literature. It is shown that the existence of a solution to the generalized version(s) of Lyapunov-Metzler inequalities is equivalent to the existence of a solution to the generalized version(s) of S-procedure characterization with a restricted choice of the scalar quantities involved in the latter. This recovers some of our earlier works on the classical Lyapunov-Metzler inequalities as a special case. We also highlight and discuss an open question of whether the generalized versions of S-procedure characterization are strictly less conservative than the generalized versions of Lyapunov-Metzler inequalities, which in turn are equivalent to periodic stabilizability as was recently shown