1Infinite-Horizon Switched LQR Problems in Discrete Time: A Suboptimal Algorithm With Performance Analysis

Abstract — This paper studies the quadratic regulation problem for discrete-time switched linear systems (DSLQR problem) on an infinite time horizon. A general relaxation framework is developed to simplify the computation of the value iterations. Based on this framework, an efficient algorithm is developed to solve the infinite-horizon DSLQR problem with guaranteed closed-loop stability and suboptimal performance. Due to its stability and suboptimal performance guarantees, the proposed algorithm can be used as a general controller synthesis tool for switched linear systems. This paper studies an extension of the classical LQR prob-lem to switched linear systems (SLS), which will be referred to as the Discrete-Time Switched LQR (DSLQR) Problem. The goal is to find both the continuous-control and switching-control strategies to minimize a quadratic cost functional ove