$H_{\infty}$ Filtering for Discrete-Time Switched Systems With Known Sojourn Probabilities

This technical note deals with the design of mode-dependent H_∞ filters for a class of discrete-time switched systems with nonlinearities. In this class of systems, when the system mode changes, the filter designed for the specific subsystem also switches accordingly. The main contribution is on the use of the information of the sojourn probability-the probability of the switched system staying in each subsystem-to build new kind of switched system model when this additional information is available. Sojourn probabilities are easier to obtain than the transition probabilities commonly used in Markovian jump systems. Applying the Lyapunov functional method, the bounded real lemma (BRL) for the resulting filtering error system is obtained in Theorem 1. The filter parameters are designed in Theorem 2 by solving a set of linear matrix inequalities. Finally, two illustrative examples are given to demonstrate the effectiveness and potential of the proposed approach.

I. Introduction

Switching systems are a class of hybrid systems consisting of a family of subsystems and a switching mechanism that specifies which subsystem is activated along the system trajectory. Many real-world processes and systems can be modeled as switched systems, including chemical processes, computer controlled systems, networked control systems and switched circuits [3], [5], [11], [12].