Abstract
In this paper, the H_{infty} performance analysis and switching control of uncertain discrete switched systems with time delay and linear fractional perturbations are considered via a switching signal design. Lyapunov-Krasovskii type functional and discrete Wirtinger inequality are used in our approach to improve the conservativeness of the past research results. Less LMI variables and shorter program running time are provided than our past proposed results. Finally, two numerical examples are given to show the improvement of the developed results.
Highlights
In recent years, the dynamical systems have often been characterized by both continuous and discrete dynamics
A switched system may be obtained from hybrid systems with only one discrete state for some x(t) [, ]
The system dynamics of switched systems are comprised of a family of continuous or discrete subsystems and a signal handling the switching among the subsystems
Summary
The dynamical systems have often been characterized by both continuous and discrete dynamics. In [ – ], some switching signal design techniques are proposed to guarantee the stability and performance of discrete switched systems with time delay. A simple method to design the switching signal in H∞ performance and switching control is proposed for discrete switched systems with time delay and linear fractional perturbations. The following state feedback switching control is used to achieve the stabilization and H∞ performance for the switched system in ( a)-( h): u(k) = –Kix(k) – Kτix(k – τ ), when σ x(k) = i, where the state feedback gains Ki, Kτi ∈ υ×n will be designed from our proposed result. The delay upper bound and switching signal in ( ) that guarantee the asymptotic stability and H∞ performance for system ( a)-( h) with ( ) are provided in Table for α = α = From these comparisons in Table , our proposed results may be less conservative than some published ones
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