Non-fragile Delay-dependent Robust Control For Uncertain Linear Delay-systems

As well known,the precondition for conventional designs of optimal and robut controllers,that the controller should be realized exactly,always results in fragile controllers,so that small perturbation of the coefficients of the designed controller destabilize the closed-loop control system.In addition,since time-delay is a normal phenomenon widely existed in many industrial process control systems,it is indeed the critical source of instability and degradation in control performance of control systems.To handle this problem,based on the Lyapunov stability theory and the new method of delay-dependent robust stability developed in recent years,the problems of non-fragile robust H_∞control and guaranteed cost control were investigated for uncertain linear systems,neutral systems,discrete systems with time-delays in this thesis.(1) Analysis on the delay-dependent robust stability of linear systems with time delays by using bisection of time-delaySo far in the study on the delay-dependent robust stability with delays, the delay information in Lyapunov-Krasovskii functional is always viewed as an integer.That is,the coefficient matrices of positive definite Q and R are constant at the interval[-h,0]in Lyapunov-Krasovskii functional.That induces conservation of the bound of delays.To overcome this shortage,the method decomposing the delay interval into two equidistance subintervals was introduced,on which different new Lyapunov functionals were defined in two intervals and two cases,with respect to the cases of d(t) with constant and time-varying delays.Numerical example was given to show that,the results were less conservative.(2) The non-fragile robust controller designed for linear systems with time delays using bisection of time-delay Based on the robust stabilization of delay systems,firstly,considering the uncertainties with state and control input,which are always in the terms of the product of two uncertainties,the non-fragile delay-dependent robust H_∞control of linear delayed systems was investigated.A new delay-dependent condition,which ensured that the closed-loop system was internally robust stable with a given H_∞disturbance attenuation levelγunder zero condition via a non-fragile controller,was obtained with respect to additive and multiplicative uncertainties.As a result,the method of non-fragile H_∞controller design was proposed.Secondly,bisection of time-delay was introduced to the non-fragile robust controller designed for linear systems with time delays using bisection of time-delay,so that,with respect to two cases of d(t) with time-invarying and time-varying delays,the new delay-dependent conditions are obtained,which could ensure that,via the non-fragile controller,the closed-loop system was internally robust stable with a given H_∞disturbance attenuation levelγunder zero condition. Numerical simulation was given to show the validity of this approach.(3) The non-fragile robust controller for neutral systems with time delaysThe problem of delay-dependent non-fragile H_∞control for neutral time-delay systems was concerned with additive and multiplicative controller uncertainties.At first,a sufficient Bounded Real Lemma condition of the closed-loop system was given to show the internally stable,and also the H_∞delay-dependent disturbance performance via a non-fragile controller. The result only depended on the solutions of linear matrix inequalities,so that no parameter needs to be tuned.Numerical simulation was given to show the validity of the proposed approach.(4) The non-fragile robust controller for discrete systems with time delays Based on an inequality method for finite sums and Lyapunov stability theory,a new delay-dependent Boundary Real Lemma was obtained,which could ensure that the closed-loop system was internally robust stable with a given H_∞disturbance attenuation level via a non-fragile controller for uncertain discrete-delay systems.Then,the design of non-fragile H_∞controller was proposed by using iterative algorithm with respect to additive and multiplicative uncertainties.It can be easily solved by linear matrix inequalities(LMI) in Matlab Toolbox.A numerical simulation was given to show the validity of this approach.(5) The non-fragile guaranteed cost controller for neutral systems with time delaysFor the neutral time-delay systems,by introducing augmented Lyapunov-Krasovskii functional,the non-fragile guaranteed cost controller was obtained.The design method of non-fragile guaranteed cost control for uncertain neutral systems with state and control input delay was discussed. The feasible solutions were proposed to non-fragile guaranteed cost controller with respect to additive and multiplicative gain disturbance. Numerical examples were given to show the less guaranteed cost performance than the existing ones.