Performance Analysis And Observer Design Of Rectangular Singular Markov Jump Systems

For many practical systems such as electronic network and constrained robot,the number of variables and the number of equations are generally differ-ent.Thus,compared with the square singular Markov jump systems,the rect-angular singular Markov jump systems have more general structure and wider applications.Besides,one-sided Lipschitz condition is weaker than the Lips-chitz condition,and the results considered the one-sided Lipschitz condition are less conservative than ones with Lipschitz condition.Based on the rectangular singular Markov jump systems,this dissertation investigates the existence of non-impulsive unique solution and stability problem for continuous-time and discrete-time linear rectangular singular Markov jump systems,and deals with unknown input observer design problem for continuous-time one-sided Lips-chitz nonlinear rectangular singular Markov jump systems.This dissertation consists of six chapters as follows.In Chapter 1,the research background of singular systems,rectangular singular systems,rectangular singular Markov jump systems,stability and ob-server are introduced.The curent status of rectangular singular Markov jump systems and unknown input one-sided Lipschitz nonlinear observer are given as well.Then,the definitions and properties of the generalized inverse.Schur complement lemma and linear matrix inequality are introduced.Last,the main work and highlights of this dissertation are presented.In Chapter 2,the sufficient and necessary conditions are proposed to guar-antee that the continuous-time linear rectangular singular Markov jump sys-tems are column regular,column impulse-free,stochast.ically stable,have a u-nique solution without,impulse when the number of the equations are not less than the number of variables(m ? n).and are row regular,row impulse-free,the differential subsystem is stochastically stable and has a unique solution without impulse when the number of variables are not less than the number of equations(m ? n).Then theses conditions are transformed to a set of linear matrix equalities,which can be easily solved.Besides,Assumptions 2.1-2.3 are introduced to tackle the common problem that the algebra subsystem of singular Markov jump systems has a jump at the instant as Markov process switches,which are easier to be verified than the method in[62].Last,three examples,including LRC circuit examples and numerical examples,are given to demonstrate that the results are effective,and the simulation is presented by the Matlab LMIs toolbox.In Chapter 3.the sufficient and necessary conditions are given to guar-antee that the discret.e-time linear rectangular singular Markov jump systems are column regular,column causal,stochastically stable,have a unique solu-tion without impulse for the case m ? n,and are row regular,row causal,the differential subsystem is stochastically stable and has a.unique solution without impulse for the case m<n.Then theses conditions are transformed to a couple of linear matrix equalities,which can be easily solved.In addi-tion,to address the common problem that the algebra subsystem of singular Markov jump systems has a jump at the instant as Markov process switches,Assumptions 3.1-3.3 are proposed.Last,LRC circuit examples and numerical examples are presented,which verifies the usefulness and practicability of the results.And the simulation is finished with the Matlab LMIs toolbox.In Chapter 4,the problem of unknown input full-order state observer for one-sided Lipschitz nonlinear continuous-time rectangular singular Markov jump systems are investigated.Combined the Lyapunov stability theorem with the matrix generalized inverse technique,the existence sufficient condition and design method of unknown input full-order state observer for one-sided Lips-chitz nonlinear rectangular singular Markov jump systems are proposed,and then the observer design problem is transformed into the feasibility problem of a set of linear matrix inequalities.Last,a numerical example is given to show the validness of the design method.In Chapter 5,the reduced-order state observer and reduced-order H?state observer design problems for one-sided Lipschitz nonlinear continuous-time rectangular singular Markov jump systems with unknown inputs are stud-ied.Based on the Lyapunov stability theorem and matrix generalized inverse technique,the reduced-order state observer and reduced-order H? state ob-server design problems are changed to the solvability problem of a couple of linear matrix inequalities,and the effectiveness of the design criteria are veri-fied by numerical examples.In Chapter 6,the main contributions of this dissertation are summarized,and the improvements which can be made in the future are presented as well.