Discounted-cost Linear Quadratic Regulation of Switched Linear Systems

Abstract

In this paper, we will investigate the design of discounted-cost linear quadratic regulator for switched linear systems. The distinguishing feature of the proposed method is that the designed discounted-cost linear quadratic regulator will achieve not only the desired optimization index, but also the exponentially convergent of the state trajectory of the closed-loop switched linear systems. First, we adopt the embedding transformation to transform the studied problem into a quadratic-programming problem. Then, the bang-bang-type solution of the embedded optimal control problem on a finite time horizon is the optimal solution to the original problems. The bang-bang-type solutions of the embedded optimal control problem is to be shown the optimization solution of the studied problem. Then, the computable sufficient conditions on discounted-cost linear quadratic regulator are proposed for finite-time and infinite-time horizon case, respectively. Finally, an example is provided to demonstrate the effectiveness of the proposed method.