Two Types Of Uncertain Systems With Guaranteed Cost Control And Robust H_ ¡Þ Control

As we know,time delays are often encountered in various practical systems, such as AIDS epidemic, chemical engineering systems, nuclear reactor,popula-tion dynamic model, ship stabilization, and systems with lossless transmissionlines. Their existence is often one main cause of instability and poor performance of sys-tems.Meanwhile, in practice uncertainty in mathematical modelling is unaviodable. Therefore, it have received significant attention to research the robust stability, guar-anteed cost control and robust H∞control problems of uncertain dynamic systems with time-varying delays in the past decades.Depending on whether the result itself contains the delay information,criteria for time-delay systems can be classified into delay-independent criterion and delay-dependent criterion. Generally speaking, the latter ones are less conservative than the former ones when the time delays are very small.In recent years,singular systems are widely focused by many researchers because they are playing an important role in practical control problems gradually, lots of results of normal systems have been generalized to singular systems one after another. In this paper,two kinds of uncertain dynamic systems with time-varying delays are separately studied guaranteed cost control and H∞control problems of uncertain singular dynamic systems with time-varying delays in state and control input,and robust non-fragile guaranteed cost control problem of uncertain dynamic systems with time-varying distributed delays. By choosing a new Lyapunov func-tionals, combined with the thought of freedom matrix, the results of guaranteed cost control and robust H∞control are proposed for uncertain singular dynamic systems with time-varying delays in state and control input;and the result of robust non-fragile guaranteed cost control are proposed for uncertain dynamic systems with time-varying distributed delays,which reduced the existing numbers of conservative in the current literatures.Finally,a numerical example is given to illustrate the feasibility of the designed method.The main conclusions in this paper are as follows:(1)Guaranteed cost control for uncertain singular dynamic systems with time-varying delays in state and control input.In the part,The paper considers guaran-teed cost control problem for uncertain singgular dynamic systems with time-varying delays in state and control input. Based on the proper Lyapunov functions,delay- dependent criteria are proposed to gurantee the robust stabilization of systems. Linear matrix inequality (LMI) optimization approach is used to solve guaranteed cost control problem. By solving the corresponding linear matrix inequality, we ob-tain the robust guaranteed cost controller which can keep the quadratic performance function to stay in a given limit.Finally, a numerical example is given to illustrate the feasibility of the designed method.(2)Robust H∞control for uncertain singular dynamic systems with time-varying delays in state and control input.In the part,The paper considers robust H∞control problem for uncertain singular dynamic systems with time-varying delays in state and control input.Based on the proper Lyapunov functional and using a new inte-gral inequality, delay-dependent robust stabilization criteria and robust H∞control are proposed for such systems in terms of Linear matrix inequality (LMIs),which is less conservative than existing results.Finally, a numerical example is given to illustrate the feasibility of the designed method.(3)Robust non-fragile guaranteed cost control for uncertain dynamic systems with time-varying distributed delays.In the part,The paper considers non-fragile guaranteed cost control problem for uncertain dynamic systems with time-varying distributed delays.Both distributed systems and the state feedback controller are assumed to have the uncertainties.Based on the proper Lyapunov functions and linear matrix inequality, a sufficient condion is proposed to assure the uncertain dynamic systems with time-varying distributed delays of robust stability and the existense of a rubust non-fragile controller,with LMI depending on the size of the delay. By solving the corresponding linear matrix inequality, we obtain the robust guaranteed cost controller which can keep the quadratic performance function to stay in a given limit.Finally, a numerical example is given to illustrate the feasibility of the designed method.