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Simultaneous LQ Optimal Control for Periodic Discrete-Time Systems

In this paper, simultaneous stabilization and simultaneous optimal design for a collection of periodic discrete-time systems via periodic constant output feedback are addressed. First, a constant output feedback design approach on simultaneous optimal control is presented for a collection of linear time-invariant discrete-time systems and a heuristic iterative linear matrix inequality algorithm is developed to compute the feedback gain. Then the result is extended to design the periodic constant output feedback gain minimizing the given performance indices for a set of periodic discrete-time systems. Numerical examples are used to demonstrate the effectiveness of the proposed algorithm.