Analysis And H_? Control Of Singular Systems With Time Delays Via State-Decomposition-Based Augmented LK Functionals

Singular systems are called generalized systems,generalized state space systems,descriptor systems,implicit systems and differential-algebraic systems.They are large-scale complex systems composed of differential equations and algebraic equations,and widely used in mechanical systems,electrical systems,power systems,aerospace systems,biological engineering and other practical applications.The stability and performance analysis of singular systems are very difficult because of the semi-state dynamic feature.Thus,the research of singular systems has attracted much attention.On the other hand,the time delays are common phenomenon,which may degrade the performance of the systems and even destroy the stability of singular systems.Thus,the research on the performance analysis and controller design of singular time-delay systems has important significance.Based on the Lyapunov-Krasovskii functional(LKF)method,most results for singular systems with time delays have been reported in the past two decades.However,due to the influence of singular matrix,it is more difficult to study singular systems with time delays than regular systems with time delays,and the obtained results have much room for improvement in both conservatism and computational complexity.In view of above problems,this dissertation studies the stability,dissipativity and H_?control of singular systems with time delays.The main results and contributions are presented as follows.(1)Stability analysis of singular systems with time delays based on the neutral model transformationFor the stability analysis of singular systems with time-varying delays,singular systems with time delays are transformed to neutral systems by the neutral model transformation.For the neutral systems,the integral terms are added to construct an augmented LKF to take more cross relationships into consideration.The derivative of the LKF is estimated by the free-matrix-based integral inequality and the relaxed integral inequality respectively,and thus two stability criteria of the neutral systems are derived,which shows a stability analysis method based on the neutral model transformation.Compared with the existing methods,this method is less conservative.(2)State-decomposition-based method for stability analysis of singular systems with time delaysFor the stability of singular systems with time delays,singular systems with time delays are transformed into differential equations and algebraic equations by using the constrained equivalent transformation,and the system state is decomposed into two parts.These parts are used to construct LKFs which do not involve with the singular matrix.Then,a state-decomposition-based method for the stability is proposed,which can provide a new idea for investigating the singular systems.On the basis of this,a stability criterion,which has less conservatism and less computational complexity,is derived.(3)The dissipativity analysis of singular systems with time delays based on state-decomposition-based augmented LKFsFor the dissipativity analysis of singular systems with time delays,an augmented LKF involved with the singular matrix is firstly constructed to derive a less conservative disspativity criterion.Then,the other disspativity criterion is presented by constructing a state-decomposition-based augmented LKF,which has less conservatism and computational complexity.For the dissipativity analysis of singular systems with time-varying delays,by constructing a state-decomposition-based augmented LKF,a disspativity analysis method is presented,which is dependent upon the criterion with less conservatism and computational complexity.(4)H_? controller design of singular systems with time delays based on state-decomposition-based augmented LKFsFor H_? control design of singular systems with time delays,an H_? performance criterion is firstly derived by constructing an augmented LKF involved with the singular matrix.On this basis,an H_? state feedback controller design method is proposed.Then,a state-decomposition-based augmented LKF is constructed to present the other H_? performance criterion,and then an H_? memory state feedback controller design method is proposed,which has better control performance compared with other traditional control methods.