The Analysis And Synthesis Of Discrete-time Singular Markovian Double-jump Systems

Singular system is more extensive than the normal system,and many practical systems can be described by the form of singular system.In recent years,the theories and practical applications of singular systems have attracted much attention of many scholars,many of the conclusions of the normal system have been extended to the singular systems.However,due to the unique nature of the singular systems,and some conclusions of normal systems can not be generalized to the singular systems.The research for singular systems have not only wide applications in practice,but also profound meanings in theory.Markovian jump system is a multi-model random switching system,whose mode takes values in a finite set and mode switching from one to another are governed by a Markov chain.In practice,there are many dynamical systems with jump in their structures and parameters because of abrupt random changes phenomenon,such as breakdowns of components,changes in the interconnections of subsystems,abrupt changes disturbance of outside,environmental condition changes,abrupt change moves of nonlinear systems working points after linearization,the different effects of the environment on systems in different control stages and so on.These abrupt changes can make stochastic fluctuations of systems in different stages.Networked control systems(NCSs)are a type of distributed control systems,where system components and plant are connected via a communication channel.The performance of NCSs is influenced by the packet transmitting rate,the length of the packet and the adoptive medium access control protocol in the network.Therefore,NCSs have some main problems:network-induced time delay,packet-dropout and packet-disorder,etc,which make traditional research methods not be applied directly into NCSs,and new control theories and methods are cried for investigation.Based on the existing results on Markovian jump systems,by using linear matrix inequalities(LMIs),this paper investigates the problem of stability and stabilization of a class of discrete-time singular Markovian double-jump systems,where mode switching is governed by two independent Markov chains.Further,an H? control design method for discrete-time singular Markovian double-jump systems is developed.Finally,a class of networked control systems with random time delays in both forward and backward communication links are considered.Its stochastic admissibility analysis and controller design are studied.The main contributions of this thesis are summarized as follows:(1)A sufficient condition for the stochastic admissibility of discrete-time singular Markovian double-jump systems is established,where transition probabilities are assumed to be completely known.To the best of our knowledge,the Markovian jump systems with two independent Markov chains have not been addressed.Thus,this paper investigates stochastic admissibility of jump systems with two independent Markov chains,which includes the existing results on Markovian jump systems with one Markov chain as special cases.Then by the system augmentation approach,two-dependent-mode state feedback controller and static output feedback controller are designed.Next,we consider the stochastic admissibility of discrete-time singular Markovian double-jump systems with generally uncertain transition probabilities.(2)Next,this paper studies the problem of H? control for discrete-time singular Markovian double-jump systems and it is shown that the state feedback controller can be derived in terms of solving a set of linear matrix inequalities(LMIs).(3)Finally,we study the networked control system with random delays,which is modeled as a special Markovian jump system,where controller-to-actuator(C-A)and sensor-to-controller(S-C)delays are represented by two independent Markov chains.To reduce the conservatism,the controller is considered to depend on two correlated Markov chains.Then a mixed H2/H? output feedback controller is designed by the obtained analysis conditions.Finally,the main work of this paper is summarized,and the potential research topics for further work are pointed out.