Robust Control For Markov Switching System Based On Free-connection Weighting Matrices

Markov switching system is estabilished to solve the problem that a single dynamic system can not accurately describe the system states with abrupt structural variation resulting from, such as failures and repairs, time delay or packet loss in different channels of a network system, the system parameters are random suddenly asjusted and modifications of the operating point of a linearized model of a nonlinear system etc. As an important class of models of the hybrid dynamic system, Markov switching system is widely used in disk drive of the computer, telecommunication, power system, and so on.At present, the main conclusions for Markov switching system are obtained based on that the transition probability matrix is assumed completely known. However, in most cases, the information of transition probabilities of Markov switching system is not exactly known due to the fact that the information of the conditional probabilities can not be detected or the cost of inspect is too high, which are major factors causing the information of conditional probabilities of some sub-systems unknown. This thesis discusses the stability, stabilization, H∞control and state estimation problems for Markov switching system with partial information on transition probabilities. The main results and innovations are listed as follows:Firstly, Stabilization controller for Markov switching system with partial information on transition probability based on free-connection weithting matrics.For a class of continuous-time Markov switching system with partial information on transition probabilities, the free-connection weighting matrix method is proposed to solve the stability and stabilization problems via considering that the sum of the elements in each row of transition rate matrix is zero. By introducing the free-connection weighting matrices to separate the unknown transition rate, the less conservative stability criterion of Markov switching system with partly unknown transition probabilities is obtained. As a result, a sufficient condition for the state feedback controller design is derived in terms of linear matrix inequalities (LMIs) and the expression of the state feedback controller is described.Secondly, H∞controller for discrete-time Markov switching system with partial information on transition probabilities based on free-connection weithting matrics.For a class of discrete-time Markov switching system with partial information on transition probabilities, the stability with Hx performance and H∞control problems are investigated based on free-connection weithting matrix method. By considering the influence of the disturbance on the system states, the augmented free-connection weighting matrices are introduced by making use of the characters that the sum of the elements in each row is one. As a result, the less conservative stability criterion and bounded real lemma (BRL) of Markov switching system with partly unknown transition probabilities are obtained. Then the sufficient conditions for designing the mode-dependent Hx controllers are derived in terms of linear matrix inequalities and the expression of state feedback controller is described.Thirdly, the stability and Hx performance analysis for continuous-time Markov switching system with partial information on transition probabilities and time-varying delay based on free-connection weithting matrics.For a class of continuous-time Markov switching system with partial information on transition probabilities and time-varying delay, the delay-dependent stochastic stability with H∞performance is investigated through taking into account the state of Markov switching system subjected to two sub-systems at the moment of sub-systems switching. As a result, based on the free-connection weighting matrix method, the novel LMI-based stochastic stability criterion and BRL for Markov switching system with time-varying delay are obtained without ignoring the effect of time-varying delay.Fourthly, state observers design for continuous-time Markov switching system with partial information on transition probabilities and time-varying delay based on free-connection weithting matrics.For a class of continuous-time Markov switching system with time-varying delay and partial information on transition probabilities, the state estimation problem is investigated in order to realize the effective estimate of system state. Taking into account the state of Markov switching system are subject to two sub-systems at the moment of sub-systems switching, the state observers are designed to estimate original systems through available output measurement based on the delay-dependent stochastic stability criterion, and furhermore the expression of state observers is described.Finally, stochastic stability for continuous-time Markov-type genetic regulatory networks (GRNs) with partial information on transition probabilities and time-varying delay based on free-connection weithting matrics.For a class of continuous-time Markov-type GRNs with transcription delay, translation delay and unknown transition probabilities, the stochastic stability problem is investigated. Taking into account the influence of different time-varying delays and the state of Markov-type GRNs which is subject to two sub-systems at the moment of sub-systems switching, the augmented free-connection weighting matrices are introduced, as a result, the novel conservative LMI-based stochastic stability criteria for Markov-type GRNs are derived without ignoring the effect of time-varying delays.