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Suboptimal regulators for discrete time jump linear system with time-multiplied performance index

This paper addresses the suboptimal regulator design problem of discrete-time jump linear system by using a time-multiplied performance index. For a given state feedback control with constant gain matrices, the time-multiplied performance index is derived and a necessary condition for such a control to minimize the time-multiplied cost is provided. A gradient-based algorithm to find a suboptimal control law is developed and some numerical results are given to show the usefulness of the theoretical results.