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This paper will investigate the infinite horizon optimal control andstabilization problems for the Markov jump linear system (MJLS) subject tocontrol input delay. Different from previous works, for the first time, thenecessary and sufficient stabilization conditions are explored under explicitexpressions, and the optimal controller for infinite horizon is designed with acoupled algebraic Riccati equation. By introducing a new type of Lyapunovequation, we show that under the exact observability assumption, the MJLS withcontrol input delay is stabilizable in the mean square sense with the optimalcontroller if and only if a coupled algebraic Riccati equation has a uniquepositive definite solution. The presented results are parallel to the optimalcontrol and stabilization for standard system with input delay.

Optimal Stabilization Control for Discrete-time Markov Jump Linear System with Control Input Delay