Lyapunov iterations for optimal control of jump linear systems at steady state

Abstract

In this paper we construct a sequence of Lyapunov algebraic equations,whose solutions converge to the solutions of the coupled algebraic Riccati equations of the optimal control problem for jump linear systems. The obtained solutions are positive semidefinite, stabilizing, and unique. The proposed algorithm is extremely efficient from the numerical point of view since it operates only on the reduced-order decoupled Lyapunov equations, Several examples are included to demonstrate the procedure. >