A Study on Generalized Invariant Subspaces and Disturbance-Rejection Problems for Periodic Discrete-Time Systems

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The project of this study consists of the following five parts.(1) The first study is to investigate about the minimal dimension of dynamic compensator which solves disturbance-rejection problems in the framework of the so-called geometric approach.(2) The second study is to introduce the concepts of the generalized invariant subspaces and to investigate the properties of those subspaces for linear uncertain periodic systems.(3) The third study is to formulate the disturbance-rejection problems with state and / or static output feedback for linear uncertain periodic systems and to obtain the solvability conditions for the problems.(4) The fourth study is to introduce the concepts of generalized (C(k), A(k), B(k))-pair and to investigate the properties of that for linear uncertain periodic systems.(5) The fifth study is to formulate the disturbance-rejection problem with dynamic compensator for linear uncertain periodic systems and to obtain the solvability conditions for the problem.As results of the above studies, some concepts of generalized invariant subspaces and generalized (C(k), A(k), B(k))-pairs for uncertain linear periodic systems were introduced and their properties were investigated. Further, the disturbance-rejection problems with state feedback, output feedback and dynamic compensators for uncertain linear periodic systems were formulated and some solvability conditions were given, respectively.