RobustH∞ filtering for switched linear discrete-time systems with polytopic uncertainties

Abstract

In this paper, the problem of robust H 1 filtering for switched linear discrete-time systems with polytopic uncertainties is investigated. Based on the mode-switching idea and parameter-dependent stability result, a robust switched linear filter is designed such that the corresponding filtering error system achieves robust asymptotic stability and guarantees a prescribed H 1 performance index for all admissible uncertainties. The existence condition of such filter is derived and formulated in terms of a set of linear matrix inequalities (LMIs) by the introduction of slack variables to eliminate the cross coupling of system matrices and Lyapunov matrices among different subsystems. The desired filter can be constructed by solving the corresponding convex optimization problem, which also provides an optimal H 1 noise-attenuation level bound for the resultant filtering error system. A numerical example is given to show the effectiveness and the potential of the proposed techniques.

Exponential H∞ filtering for switched linear systems with interval time‐varying delay

“…If there exist positive-definite symmetric matrices P il , Z il , Q ik , P jl , Z jl , Q jk and matrices (26), (27), (29) and the following inequality holds:…”

“…The proof is completed. (27) and * = 0 by (29), then the filtering error system (5) possesses a common Lyapunov functional and the switching signals can be arbitrary. This implies that system (5) under the arbitrary switching signals is exponentially stable with a prescribed H ∞ attenuation level .…”

Robust Consensus for a Class of Uncertain Multi-Agent Dynamical Systems

“…Moreover, we have shown how these conditions can be easily investigated through convex programming by using standard software. Various future directions can be taken starting from the results proposed in this paper, for instance one can consider switching topology adopting the frameworks introduced in [20], [21] and LMI techniques for switching systems as the one introduced in [22]. Also, multi-agent dynamical systems with rational dependence on the uncertainty and/or time-varying uncertainty can be considered adopting the methodology proposed in [23].…”

Fault detection for switched systems with finite-frequency specifications

“…Switching control has been applied in a wide range of the physical and engineering systems, such as aircraft multi-mode control [4], missile autopilot design [5], and spacecraft formation control [6]. Several approaches for the filter design have been proposed, such as multiple Lyapunov functions approach [7], dwell-/average dwell-time approach [8][9][10][11], switched Lyapunov function approach [12,13], etc.…”