H∞ controller design for a class of multirate systems using a switched control method

Abstract

This paper deals with H∞ controller design for a linear multirate system with two sampling rates via a switched control method, in which the ratio of two sampling rates is assumed to be a rational number. A periodic switched controller is constructed based on whether the sampled-data of state variables at two sampling rates are available simultaneously or separately. The closed-loop system is modeled as a switched system with subsystems that have different input delays. Using a Lyapunov-Krasovskii functional method, a delay-dependent criterion is derived to such that the switched system is exponentially stable with a prescribed H∞ performance. A numerical example is provided to illustrate the effectiveness of the proposed method.