Robust <i>H</i>_∞ Controller Design of Switched Delay Systems with Linear Fractional Perturbations by Synchronous Switching of Rule and Sampling Input

Abstract

In this paper, we propose synchronous switching of rule and input to achieve H∞ performance for an uncertain switched delay system with linear fractional perturbations. Our developed simple scheme utilizes the linear matrix inequality optimization problem to provide a feasible solution for the proposed results; if the optimization problem was feasible, our proposed robust H∞ control could be designed. The feasibility of the optimization problem could be solved using the LMI toolbox of Matlab. In this paper, robust control with sampling is proposed to stabilize uncertain switching with interval time-varying delay and achieve H∞ performance. Interval time-varying delay and sampling were considered instead of constant delay and pointwise sampling. A full-matrix formulation approach is presented to improve the conservativeness of our proposed results. Some numerical examples are demonstrated to show our main contributions.

Keywords

• <i>H</i>_∞ performance
• interval time-varying delay
• switched delay system
• switching rule
• synchronous switching
• sampling input