Analysis Of Controllability And Stability And Rough Control Of Linear Time Varying Periodic Systems

Linear time varying periodic (LTVP) systems can be found in many engineering technology field, such as flexible mechanics system, parameter resonator, proton ac-celerator, celestial mechanics, laser physics, satellite gesture control, helicopter drive system, ecosystem, economic system, period environment competition balance etc. Linear time varying periodic systems are a class of systems that are very important but have less research results. The rough set (RS) theory is a new mathematical tool to deal with imprecise, incomplete and inconsistent data. It can find hidden knowl-edge and explain latent rules from itself data. Rough set theory provides theory base for expert control and intelligence control. With the thought of linear system theory and modern robust control theory, and the method of rough set theory, the analy-sis of controllability, observability, asymptotic stability, Riccati stability and rough control, networked control of LTVP systems are considered. The main contents of the dissertation can be briefly described as follows:1. The effective algorithms of rough set data analysis are presented and im-proved. The method of coding and scanning objects is considered. The algorithm complex degree is reduced. The heuristic attribute reduction algorithm with at-tribute importance, based on discriminative matrix attribute reduction algorithm, hierarchic analysis attribute reduction algorithm, variable precision attribute reduc-tion algorithm and interval number attribute reduction algorithm are presented.2. By using MATLAB as the development language, the simulation tool box software of rough set data analysis is firstly programmed, including heueristic at-tribute reduction algorithm, disceraisility matrix attribute reduction algorithm, vari-able precision attribute reduction algorithm and interval number attribute reduction algorithm. The program of upper approximation, lover approximation realization equivalence relation, relatively attributes reduction, attribute core, etc. are ob-tained. The graphic user interface is designed. The deficiency of MATLAB software at rough set tool box aspect is filled up.3. The new necessary conditions of controllability of LTVP systems are ob-tained. The method has feasibility and is more convenient. It dose not need cal-culating the state transition matrix. The controllability of time varying descriptor systems is discussed. An error conclusion of controllability of LTVP systems in the journal of IET control theory and application is pointed out by an example. By duality, all the obtained results can be extended the corresponding observability results.4. The necessary and sufficient conditions of Riccati stability of linear time in-variant (LTI) systems are given. The method only depends on the system structure, without the calculation of LMIs feasibility. The necessary and sufficient conditions of Riccati stability of LTVP systems are provided. The applications of Riccati stability of LTI systems in time delay systems and robust control systems are demonstrated by two examples. The memoryless state feedback controller, robust controller and H∞controller of LTVP systems are designed. The stability of LTVP time delay systems is analyzed.5. Survey and summary of rough control and networked control systems are provided. The method of rough control and selection of fuzzy member function are introduced. The control and simulation of networked control inverted pendulum are discussed. The stability of LTVP networked control systems is analyzed and the controller of LTVP networked control systems is designed. The relation between generalized positive definite and stability is discussed. A mistake on generalized positive definite application is pointed out.