Guaranteed-cost H_∞ Robust Control For Uncertain Systems With Time-delay

It is well know that time-delays as well as uncertainties are frequently the main cause of deterioration of systems performance and instability of systems. Therefore, how to designing controllers which make uncertainty systems with time-delay be stable and guarantee an adequate level of performance, which is a hot research field, has theoretic and practical significance.Based on Lyapunov stability theory, using linear matrix inequality (LMI), approach and particle swarm optimization (PSO) algorithm, the guaranteed-cost H_∞robust control problems of the linear fractal uncertainty systems with time-delay are studied by introducing free-weighting matrix in this paper. The main contents are as follows:1. To uncertainty systems with state and control input time-delay, a sufficient and necessary condition is given for stability of the closed-loop system. And the guaranteed-cost H_∞robust controller is designed. Then the relationship between quadratic cost upper bound and H_∞performance index is established.2. By constructing feasible Lyapunov function and using integral inequality, the problems of robust non-fragile H_∞control and guaranteed-cost H_∞robust non-fragile control for a class of time-varying delay uncertain linear systems are investigated. Furthermore, combining LMI and PSO algorithm, a method to calculate the free parameters is proposed. For the results don't require the derivates of the time-delay functions, the design methods are still validity for fast time-varying delay.3. When fault appears in sensor or actuator of the systems, the sufficient existence condition of guaranteed-cost H_∞robust fault-tolerant control low is inducted. Also, the controller which could not only make system stable but also guarantee a prescribed H_∞performance and a quadratic cost upper bound of the resulting closed-loop system is designed.4. Based on Takagi-Sugeno (T-S) fuzzy model, the problems of robust H_∞control, guaranteed-cost control and guaranteed-cost H_∞robust control for nonlinear uncertainty systems with time-varying delay are studied by using new type Lyapunov function and introducing a lot of free-weighting matrixes. The Truck-Trailer model is chosen as simulating model to illustrate the effectiveness of the proposed approach.