Impulsive Observer And Observer-based Control Using Time-Varying Gains

Since the theory of impulsive observer proposed by German scholars Raff and Allg ¨ower at the beginning of this century,the frame of observerbased output feedback control has become one of the important control strategies in the field of control engineering.Impulsive observer is committed to obtaining the estimation of state of controlled system by combining the output information of discrete times with its correction terms.Under the background of networked control,the states of system are affected by delays between transmissions,external disturbances and other factors.There are of great significance that how to design an effective impulsive observer to estimate the state of original system and how to explore the output feedback control based on impulsive observer.In this thesis,the impulsive observer design of Lipschitz nonlinear systems,the impulsive synchronization of reaction-diffusion neural networks systems with time-delay and the impulsive observer-based feedback control of uncertain linear time-delay system are studied,respectively.Compared with the existing methods of Luenberger-type impulsive observer,the impulsive observer designed in this thesis is a novel one with time-varying gain matrix based on the partition method.The novel impulsive observer can precisely to adapt to the variation of sampling intervals,thus improving observation accuracy and synchronization performance.The main work of this thesis is summarized as follows:(1)A novel impulsive observer-based control on partition method for a class of Lipschitz nonlinear systems is studied.Assuming that the state information of system is aperiodic and can not be completely measurable,impulsive observer based on maximum impulse intervals partition is proposed.Due to the uncertainty of the magnitude of impulse intervals,the time-varying gain matrix dynamically changes with the increasing of the number of partition.And the state of observer updates according to the mode of upgrade of the impulses.The method of LPV approach and piecewise time-varying Lyapunov function are used to analyze the exponential stability of the corresponding error system.Sufficient conditions for the stability of error system are derived in terms of linear matrix inequalities(LMIs).(2)The impulsive synchronization problem of a class of reaction-diffusion neural network system is studied.Assumed that state information of system is aperiodic and can not be completely measurable,which is different from the previous impulsive synchronization strategy based on static gain matrix.Time-varying impulsive synchronization gain matrix can adapt to variation of sampling intervals and reflect the information of impulse intervals effectively,which reducing the conservativeness of the existing results greatly.Stability of the synchronization error system is analyzed by using discrete timedependent Lyapunov function.By using a set of linear matrix inequalities,sufficient conditions for the existence of impulsive synchronous controller are given.(3)Impulsive observer-based control using time-varying gain of uncertain time-delay linear systems is studied.Firstly,impulsive observer based on time-varying gain matrices by using the sampling output information is proposed.Secondly,introducing the estimation state vector.Finally,by constructing the time-varying Lyapunov functional and combining the technology of Young inequality,the global exponential stability of error system is analyzed.(4)The design of impulsive observer for a class of Lipschitz nonlinear systems with delayed measurement and the stabilization problem of the observer-based output feedback control are studied.Assumed the upper bound of delays do not exceed the length of impulse intervals.Firstly,the controlled system is modeled as a switching system using the augmentationbased switching impulse approach.Secondly,the variable state of error is introduced to describe the closed-loop system with characteristics of hybrid structure under the feedback control.The switching time-varying Lyapunov function method and Gronwall inequality are used to analyze the stabilization of closed-loop system.Finally,the design criterion of output feedback control law based on impulsive observer is given in the form of linear matrix inequality(LMIs)with convex combination technique.