H_∞ Control And State Estimation Of Systems With Mixed Time-Delays

The phenomenon of time delay is frequently encountered in many practical systems such as mine power systems,mechanical systems,network control systems,and genetic regulatory networks and other fields.It is well recognized that the existence of time delays often causes poor performance,oscillation,or even instability.Due to different occurrence mechanisms,time delay has multiple forms of performance,and different forms of time delay have different effects on system performance.On the other hand,due to the limitation of physical equipment or the influence of external disturbance,it is impossible to obtain all the state information of the system.To improve this situation,the state estimation method can be used to estimate the unmeasurable signals in the system or restore the real signals disturbed by external disturbance.Therefore,it is of great theoretical and practical significance to study the control and state estimation of systems with mixed delays and external disturbance.Based on Lyapunov stability theory and H_∞control theory,the issue of H_∞control and state estimation for linear system and recurrent neural networks with mixed time-delays is investigated by utilizing linear matrix inequality and integral inequality techniques in this dissertation.The main innovative work of this dissertation is summarized as follows:(1)The issue of stability and H_∞control for a class of linear systems with interval time-varying delay and external disturbance is investigated.First,the interval time-varying system model with external disturbance and uncertainty is established.Then,by considering more information about the lower bound of time-delay,a newly augmented L-K functional containing multiple integral terms is constructed.Meanwhile,the Wirtinger-based inequality,auxiliary-function-based integral inequality and extended reciprocally convex are used to estimate the derivative of the constructed L-K functional accurately.Finally,the delay-dependent stability criteria with less conservatism are derived to ensure that the considered system is asymptotically stable with desired H_∞performance level.On this basis,the gain matrix of the H_∞controller is further given.(2)The problem of H_∞state estimation for a class of local field neural networks with both discrete and distributed time-delays is considered.First,the state estimator model with mixed time delays and external disturbance is established.Then,a novel L-K functional is established by including two new delay-product-type terms,multiple-integral terms and more activation function information.Meanwhile,the boundary of the activation function is divided into two subintervals to combine the constructed L-K functional effectively.Finally,by utilizing the generalized free-weighting matrix inequality and polynomial-based inequality,some new sufficient conditions are obtained such that the estimation error system is asymptotically stable with desired H_∞performance level.(3)The H_∞state estimation for a class of static neural networks with both discrete and leakage delays is studied.First,this dissertation constructs a more accurate state estimator model with mixed delays and external disturbance.To exploit the more information and relationship of delay interval,a new parameterized delay interval method is proposed by introducing two adjustable parameters.Then,an appropriate L-K functional including new non-integral DPT terms and augmented terms is constructed by combining four delay intervals.Meanwhile,for the sake of cooperating with the constructed L-K functional effectively,generalized free weighting matrix integral inequality and the improved convex combination method are utilized to estimate the derivatives of functionals.As a result,a novel criterion is obtained to ensure that the estimation error system is asymptotically stable with prescribed H_∞performance.(4)The issue of H_∞control for a class of local field neural networks with time-varying delay and external disturbance is addressed.Considering the fact that the state information of neurons is difficult to be completely obtained in practical applications,and the limitations of using the state of neurons directly as feedback signals for controller design,a new H_∞controller design approach is proposed by using the estimated state as feedback signals,and the state estimator and controller model of the system are established.Then,by establishing an appropriate L-K functional with single and double integral terms and applying some effective integral inequalities,the state estimator is presented.Meanwhile,based on the estimated state,a new H_∞controller is further developed.Finally,by utilizing an improved decoupling technique,a novel criterion is obtained in terms of LMIs,which ensures that the considered system is asymptotically stable with the given H_∞performance level.(5)The application of H_∞control and state estimation methods in engineering practice is investigated.For three practical examples of mine power system,level control of quadruple-tank process system and genetic regulatory networks,based on their dynamic models,the corresponding linear system with interval time-varying delay,delayed local field neural networks model and delayed static neural networks model are established,respectively.The state estimator and controller with given performance level are designed by using the H_∞control and state estimation methods proposed in this dissertation.Finally,the work of this dissertation is summed up,and the promising future of H_∞control and state estimation problem for systems with mixed time-delays is expected.There are 27 figures,14 tables and 188 references.