Control of linear periodic discrete-time systems

This dissertation involves the study of the control of linear periodic discrete time systems (LPDS), and especially focuses on the stabilization and the non-interacting control.;For the stabilization problem, a now control method based on the lifting technique is proposed. It is called sampled measurement periodic hold control (SMPHC). In the SMPHC framework infrequent measurements and some specific periodic holder are introduced. Then the closed loop system is transformed into linear time invariant system (LTIS). This fact is useful for designing the control law for LPDS because of various results for LTIS can be utilized. Note that the words "sample" and "hold" are only used in the above notion in this thesis and so their meanings are different from "digital control of continuous time system". For the non-interacting control problem, extensive studies has been conducted and various solvability conditions have been given for LTIS. These results we also extended to linear time varying systems or nonlinear systems. But for LPDS, few results have been given. In this thesis, the block non-interacting control problem is considered by extending the geometric approach for LTIS to LPDS.;Contributions for the stabilizing problem and the non-interecting control in this thesis are described and resulted as follows. (1) The necessary and sufficient, condition for the pole assignment problem by SMPHC and the explicit procedure for calculating the feedback gain we given. (2) Generalizing the pole assignment problem, the transition matrix assignment problem is formulated. The necessary and sufficient solvability condition for this problem is given. Moreover for the output feedback case, the explicit procedures to calculate the control low based on the observer are also given. (3) In the case of the state feedback and the measurement feedback the necessary and sufficient conditions for the block non-interacting control problem are given in the framework of the geometric approach. (4) For the output feedback case, it is also shown that the SMPHC stabilizes the closed loop system with preserving the block non-interacting property.;Throughout this thesis, some simple numerical examples we also given.