Finite-Time $$H_\infty $$ H ∞ Model Reference Control for Linear Systems Based on Average Dwell-Time Approach

Abstract

This paper investigates the problem of state tracking for model reference control in a linear system with average dwell-time approach in a finite-time interval. Both matched and unmatched cases are taken into consideration in the system. The switching law is designed by the state error such that the considered tracking error is finite-time bounded and the considered system achieves a weighted $$H_\infty $$ performance for the exogenous disturbance. With the aid of an error Lyapunov-like function and Schur complement lemma, the design of the switching law is formulated by linear matrix inequalities with sufficient conditions. A variable average dwell time is obtained that it is less than the traditional average dwell time in a finite-time interval. Finally, a numerical example is given to illustrate the effective design method of the switching law.