Control Design Method for Obtaining Special Performances in Discrete-Time Linear Switched Systems with Time-Varying Delay Based on the Average Dwell-Time Approach

This paper devotes to propose control design methods imposing general quadratic and bounded peak to peak gain performances on discrete-time linear switched positive systems with time-varying delay. General quadratic constraints are limitations that are modeled as a quadratic matrix to make a relationship between exogenous input and output signals. Moreover, the problem of bounding outputs peak amplitude for bounded disturbance inputs is named bounded peak to peak gain performance. Sufficient conditions are derived for the existence of a set of state feedback controllers guaranteeing the closed-loop switched system with time-varying delay in states not only is positive and globally uniform exponential stable but also has two stated performances for switching signals with an average dwell-time, which is greater than a positive certain constant. By using the Lyapunov-Krasovskii functional theorem, these conditions are formulated in terms of linear matrix inequalities. The quadruple tank system model is employed to illustrate the effectiveness of the proposed method.