Study Of Control Problems For Singular Markovian Jump Systems  Posted on:20161019  Degree:Doctor  Type:Dissertation  Country:China  Candidate:L Li  Full Text:PDF  GTID:1318330482955704  Subject:The system complexity theory  Abstract/Summary:  PDF Full Text Request  Currently, although much effort has been made in control for singular Markovian jump systems, results on this topic are much fewer than those on normal Markovian jump systems. Many unsolve problems need to be studied for this kind of systems. In this dissertation by using the theory of the matrix analysis and the linear matrix inequality (LMI) technique, the problem of control for singular Markovian jump systems is studied, which is motivated by the descriptor system theory, the stochastic system theory and the advanced robust control theory. Main contributions are summarized:(1) The problem of H? fuzzy control for a class of nonlinear timedelay singular Markovian jump systems is discussed. H? fuzzy control for a class of nonlinear timedelay singular Markovian jump systems with partially unknown transition rates is studied first, this class of systems under consideration can be described by TakagiSugeno (TS) fuzzy models, fuzzy state feedback controllers are designed such that closedloop systems are not only regular, impulsefree and stochastically stable, but also satisfy a prescribed H? performance in terms of LMIs. And this kind of systems with completely known transition rates can be viewed as a special case of the ones we consider here. Then by the method of the augmented matrix, the problem of H? fuzzy control for this kind of systems with completely known transition rates is discussed. When the number of fuzzy rules is relatively large, the quality of the computation for the condition obtained is greatly reduced.(2) The problem of finitetime H? control for singular Markovian jump systems is discussed. Finitetime H?, control for a class of singular Markovian jump systems with partially unknown transition rates based on the state feedback is studied first, sufficient conditions on the stochastic singular finitetime boundedness of singular Markovian jump systems with partially unknown transition rates are obtained, then results are extended to the analysis on the stochastic singular finitetime boundedness of singular Markovian jump systems with completely known transition rates. Then state feedback controllers are designed to ensure the stochastic singular finitetime boundedness and the stochastic singular H? finitetime boundedness of underlying closedloop systems in forms of strict LMIs. At last, the design of finitetime H? control for singular Markovian jump systems is studied via the static output feedback.(3) By the method of the augmented matrix the problem of robust fuzzy finitetime control for nonlinear singular Markovian jump systems is discussed, this class of systems under consideration can be described by TS fuzzy models. The designed algorithm for the state feedback controller is provided to guarantee the stochastic singular finitetime boundedness and the stochastic singular H? finitetime boundedness for closedloop systems of singular Markovian jump systems in terms of strict LMIs with a fixed parameter. Then the method is extended to the designed algorithm for the static output feedback controller of singular Markovian jump systems.(4) The problem of fuzzy stochastic optimal guaranteed cost control for a class of bioeconomic singular Markovian jump systems is discussed. By considering the price coefficient to be influenced by a Markovian process, a bioeconomic singular Markovian jump model is established, then the model is described by the TS fuzzy singular Markovian jump system. A new design method of fuzzy state feedback controllers is presented to ensure not only the regularity, nonimpulse and stochastic singular finitetime boundedness for closedloop systems of this kind of systems, but also an upper bound achieved for the cost function in forms of strict LMIs. Finally this model is applied to the practical example of the elver breeding.(5) The problem of robust finitetime H? control for a class of uncertain singular stochastic Markovian jump systems with partially unknown transition rates via proportionaldifferential control law is discussed. Uncertainties are not only in state matrices and input matrices, but also in differential matrices. The stochastic finitetime stability for singular stochastic Markovian jump systems is defined. Based on this definition, sufficient conditions for control laws designed are established to guarantee the stochastic finitetime stability for closedloop systems of singular stochastic Markovian jump systems with partially unknown transition rates and the H? performance satisfied. Numerical examples show the effectiveness of the new definition.(6) The problem of the sliding mode control design for singular stochastic Markovian jump systems with uncertainties is studied. A suitable integral sliding function is proposed, a new sufficient condition is developed which not only guarantees the stochastic admissibility of the sliding mode dynamics, but is also constructive and determines all the parameter matrices in the integral sliding function. Then a sliding mode control law is synthesized such that the reachability of the specified sliding surface can be ensured. Finally results developed are extended to the sliding mode control design of stochastic Markovian jump systems.  Keywords/Search Tags:  Singular Markovian jump systems, TS fuzzy singular systems, Stochas tic systems, Timedelay systems, Linear matrix inequality(LMI), State feedback con troller, Static output feedback controller, H_? control, Guaranteed cost control  PDF Full Text Request  Related items 
 
