On the effects of redundant inputs on linear quadratic optimal control for Markov jump linear systems

This paper investigates the linear quadratic (LQ) optimal control problem for continuous-time Markov jump linear systems (MJLS). Although LQ optimal control problem of MJLS has been extensively studied, the impact of introducing redundant inputs remains insufficiently explored. In this work, we analyse the influence of redundant inputs on the LQ performance of MJLS. First, a monotonically decreasing sequence providing upper bounds and a monotonically increasing sequence providing lower bounds for the positive semi-definite solutions of the continuous coupled algebraic Riccati equations (CCARE) is constructed. Based on these bounds, two sufficient conditions are derived to ensure reductions in both the quadratic performance index and the norm of the optimal feedback gain matrix. Finally, numerical simulations validate the theoretical results and demonstrate that systems with redundant inputs achieve better control performance.