Decentralized Derivative Feedback Control For Interconnected Descriptor Systems

Interconnected descriptor system is a kind of dynamic systems with special structures and has a wide range of applications,such as economic systems,electrical networks,power systems,chemical processes and so on.Interconnected descriptor systems form contains the standard interconnected statespace systems form as a special case and can represent a much wider class of systems than the standard interconnected state-space systems counterpart.It is of ten convenient and natural to model many practical systems by using interconnected descriptor systems.In recent years,the theory and application of the interconnected descriptor systems have attracted much attentions of a great many scholars.However,because of structural particularity and the existence of impulsive terms contained in the solutions,the research on the interconnected descriptor systems is much more difficult and interesting than that of the standard statespace systems or descriptor systems.At present,the results of interconnected descriptor systems are relatively few,and many related problems still need to be further studied.Based on decentralized control theory and matrix theory,we start with the stability analysis of interconnected descriptor systems.Then the problems of robust stability and stabilization for uncertain interconnected nonlinear descriptor systems are studied.Following that,we investigate the problem of impulse elimination for descriptor systems by utilizing derivative output feedback.Furtherlmore,the problems of impulse controllability and impulse observabil-ity for interconnected descriptor systems are studied by utilizing derivative feedback.In the end,the problems of impulse controllability and impulse observability for descriptor complex network are discussed based on derivative feedback.The main contributions of dissertation are as follows.(1)The background of this dissertation is introduced.The research significance and development of the complex large systems,descriptor systems and interconnected descriptor syste,ms are introduced in detail.(2)The proroblem of adnmissibility for interconnected descriptor systems is investigate based on the matrix trace inequality.A nexw suicient condition for admissibility of interconnected descriptor systems is obtained,and the corresponding decentralized state feedback controller is design.Different from the existing methods,the given approach in this dissertation overcomes the constrain on Lyapunov matrix which must be block diagonal in the previous literature when the decentralized controller is designed.Our approach is more general.(3)The problems of robust stability and stabilization for uncertain interconnected nonlinear descriptor systems are mainly studied.By using Differential Mean Value Theorem,we transform nonlinear descriptor systems into linear parameter varying systems.Then a sufficient condition of quadratic normality and quadratic stability of the closed-loop system is given by using the Lyapunov and LMI methods.Based on that,a decentralized proportional plus derivative state feedback controller and decentralized proportional plus derivative output feedback controller are designed,respectively.The designed controller can guarantee the resulted closed-loop system to be quadratically normal and quadratically stable.Compared to the other methods,a larger feasible region can be obtained by using Differential Mean Value Theorem.It should be pointed out that the considered nonlinear descriptor systems can be transformed into an equivalent linear parameter varying systems while the other methods can only be applied into the analysis of system performance.(4)The problems of impulse elimination and controller design for descriptor systems are studied by derivative output feedback.Based on a novelly restricted system equivalence between matrix pencils,some sufficient conditions of the impulse elimination for descriptor systems with the range of different dynamical orders of the resultant closed-loop system are given.We analysis the possible dynamic orders of the descriptor systems based on the derivative output feedback controller.Based on that,we design the derivative output feedback controller for descriptor systems according to the different dynamical orders of the resultant closed-loop system.The major difference between the proposed method and the other methods is that maximum dynamic order for the closed-loop system is not necessarily required when the problem of the impulse elimination of the considered closed-loop system can be solved.(5)The problems of impulse controllability and impulse observability for interconnected descriptor systems with two subsystems are mainly studied by the derivative state feedback and the derivative output feedback,respectively.Based on singular value decomposition,some necessary conditions which ensure the resultant closed-loop system under the conditions of the derivative state feedback and the derivative output feedback respectively to be impulse controllable or impulse observable are derived,by utilizing the inequalities of matrix rank.The given conditions are easy to be solved.At the same time,the design methods of the derivative state feedback controller is proposed and the parametrization of controllers are given.The given methods have no constrains on the derivative coefficient matrix of the considered systems,and the proposed results are more general.Since the method of the singular value decomposition is used,the good numerical stability is possessed.(6)The problem of impulse controllability for descriptor complex network is studied by decentralized proportional plus derivative output feedback.We first transform the considered descriptor complex network model into a nonlinear interconnected descriptor systems.Then we use Differential Mean Value Theorem to transform the nonlinear model into linear parameter varying systems.As a result,the considered problem can be transformed into the study on the impulse controllability for linear parameter varying systems.Based on relationship between the ranks of matrices,a sufficient condition which ensures the impulse controllability of the resultant closed-loop system is derived,and the design of the corresponding decentralized proportional plus derivative output feedback controller is also provided.Finally,the results of the dissertation are summarized and further research topics are pointed out.