A Study on Generalized Invariant Subspaces and Robust Disturbance-Rejection Problems

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The project of this study consists of the following five parts.(1) The first study is to introduce the concepts of generalized invariant subspaces for uncertain linear finite-dimensional systems and to investigate the relationship between the special finite set of linear systems and a given uncertain linear system in the framework of the so-called geometric approach.(2) The second study is to investigate some fundamental properties concerning the generalized invariant subspaces and to formulate the disturbance-rejection problems with output feedback and / or dynamic compensator. Further, it is to obtain the solvability conditions for the problems.(3) The third study is to introduce the concepts of generalized invariant subspaces for uncertain linear infinite-dimensional systems and to investigate their properties.(4) The fourth study is to formulate the disturbance-rejection problems with state and / or output feedback for infinite-dimensional systems and to obtain the solvability conditions for the problems.(5) The fifth study is to formulate the disturbance-rejection problem with dynamic compensator for infinite-dimensional systems and to obtain the solvability conditions for the problem.As results of the above studies, some generalized invariant subspaces for uncertain linear finite- and/or infinite-dimensional systems were introduced, respectively and their properties were investigated.Further, the disturbance-rejection problems with state feedback, output feedback and dynamic compensator were formulated and some solvability conditions were given.