LMI-Based Stability Analysis and Controller Design for Periodic Linear Time-Varying Systems

A method for determining whether a linear time-varying (LTV) system is exponentially stable has been proposed based on differential Lyapunov inequalities (DLIs). However, there are few established systematic methods to find solutions of DLIs. In this paper, we focus on a class of periodic LTV systems and propose a method to find solutions of DLIs by using linear matrix inequalities (LMIs). Moreover, we propose a method to design state observers, state feedback controllers and output feedback controllers for periodic LTV systems by utilizing the proposed DLI solutions search method. Some examples show the effectiveness of the proposed analysis and design method.