Observer Design For Interval Time-varying Time-delay Dynamic Systems

Observer design problem is an important research topic in control theory.When not all the states of the system are measurable due to various reasons,it is required to design an observer to estimate the states of the system and replace the true states with the estimated states,which is necessary to ensure the implementation of various control designs.On the other hand,the phenomenon of time delay is widespread in various engineering practical systems,and it usually leads to the performance degradation and even the instability of the controlled system.Therefore,the research on the observer design problem of time-delay systems has theoretical and practical value.Compared with the system without time-delay,the observer design and stability analysis for time-delay systems,especially interval time-varying delay systems,are more complicated.Based on the current research findings of observer design problem,this thesis will utilize Lyapunov stability theory and various inequality techniques to study the observer design problem for several classes of dynamic systems with time-varying delay and propose new observer design approaches.The main results of this thesis are as follows.1.The problem of H_? reduced-order observer design for a class of generalized Lipschitz nonlinear time-delay systems with disturbance inputs is studied.The nonlinear terms of considered generalized Lipschitz nonlinear time-delay system only satisfy the quadratically inner-bounded condition.Based on a state linear transformation,a reduced-order time-delay nonlinear observer with special structure is derived.All observer parameters are exactly parameterized by a free matrix.The observer design problem is reduced to the stability analysis problem of the estimation error system with time-delay.The H_? filtering scheme is used since the disturbance input is considered.By selecting a appropriate Lyapunov-Krasovskii functional and employing a newly proposed extended reciprocal convexity inequality which is proved to be more strict than the traditional reciprocal convexity inequality,some new and less conservative synthesis conditions of observer design which can be tackled by Matlab tool box directly are presented for nonlinear systems with interval time-delay.The free matrix can be computed as the same time,and then all the parameters of the presented observer are also computed.Due to considering more relaxed conditions,wider range of time delay,and more strict inequality,the obtained results are less conservative and applicable to a larger class of nonlinear systems.Numerical examples further illustrate the superiority of the proposed scheme.2.The problem of H_? full-order observer design for a class of one-sided Lipschitz singular nonlinear systems with interval time-varying delay and disturbance inputs is studied for the first time.The observer design problem for one-sided Lipschitz singular nonlinear system with time-delay is complicated and it has not been reported by now.The time-delay singular nonlinear systems considered in this thesis satisfy both the one-sided Lipschitz condition and the quadratically inner-bounded condition,which include the traditional Lipschitz condition as the special case,so it is a broader class of systems.We use the matrix equation theory and Lyapunov stability theory,and employ the filtering scheme to develop the observer design scheme for singular nonlinear systems with time-delay in both discrete-time and continuous-time cases.For one-sided Lipschitz discrete-time singular systems with interval time-varying delay,a time-delay nonlinear observer with multiple parameters is constructed.By subtly introducing two auxiliary variables,the coupling matrix equations of the observer parameters are decoupled into linear matrix equations,and all observer parameters are represented by the same free matrix parameter.The problem of the observe design is reduced to the determination of the free matrix parameter to ensure the resulting estimation error dynamic system is asymptotically stable when there is no disturbance input and satisfies H_? performance when there is disturbance input.By constructing the augmented Lyapunov-Krasovskii functional and applying several important inequalities to deal with the time delay,the delay-dependent solvable conditions in LMI form of observer design are obtained,and the free matrix parameter is also computed,so that all matrix parameters of the proposed observer can be computed.In addition,for the delay-free discrete-time singular nonlinear systems,the observer design scheme is also considered,and the sufficient condition for the observer design is given.The proposed approach can also be applied to rectangular systems,thereby having a wider range of applications.Simulation examples illustrate the effectiveness of the proposed observer design approach.For one-sided Lipschitz continuous-time singular systems with interval time-varying delay,we propose an observer having the similar structure with that for the discrete-time case.By constructing a appropriate Lyapunov-Krasovskii functional and employing an important inequality named free-matrix-based integral inequality,the delay-dependent conditions with less conservativeness are presented.In addition,the sufficient condition of the observer design for singular nonlinear systems without time delay is also given.When the system is reduced to a standard time-delay one-sided Lipschitz nonlinear system,the proposed method is still applicable.The numerical examples illustrate the effectiveness and less conservativeness of the proposed method.3.The functional observer design is studied and functional observer-based actuator fault diagnosis is addressed for linear systems with time-varying delay.Nearly all the existing results concerning fault diagnosis are presented for delay-free systems,and very little work has been reported for time-delay systems.Firstly,a new method to design the low-order functional observer estimating the partial states for linear systems with time-varying delay is presented.Conditions for the existence of proposed observer and the stability of resulting estimation error dynamics are derived.Based on the proposed observer,a novel residual generator is constructed to detect actuator faults.Furthermore,a bank of residual generators for fault isolation are also constructed for time-delayed systems.The simulation results of the numerical example demonstrate that the proposed observer-based fault diagnosis scheme works effectively.