Robust Stability With Time-varying Delay Neutral Systems Analysis And H_ ¡Þ Control

Uncertain nonlinear system with time-delay always exists in practical industry control systems. There are many wide applications in engineering and improving the performance of control systems. Also, time-delay is the sources of instability and poor performances of systems. Therefore, the researches on the stability analysis and robust H∞control problem of uncertain systems with time-delay has theoretical and practical significance. In recent years, since the focus of many researchers, there are many results, which are robust stability and robust controller design of neutral systems in research domain. However, because of complexity of structure, it is diffi-cult to research robust stability analysis and robust H∞control of neutral system. In order to further improve the results, we should do further'study. Particularly, how to decrease the conservatism of neutral systems is one of the focus problem of theoretical control studies.The main contents in this paper are as follows:(1)The stability criterion for uncertain neutral delay differential systems with time-delay is investigated. And the considered system have time-varying structured of uncertainty and time-varying delay. Based on Lyapunov-Krasovskii function and linear matrix inequality(LMI)techniques, combining free weighting matrices, the sufficient condition of delay-dependent stabilization for neutral systems is derived, which reduce the conservative property of some literatures. Finally, numerical ex-amples show the effectiveness of our result and much less conservative.(2)The robust stabilty condition for a class of uncertain neutral systems with time-varying and nonliner uncertainties are investigated. And uncertainties are con-sidered under the nonlinear time-varying parameter perturbus. Through choosing the appropriate Lyapunov-Krasovskii function and using Newton-Leibniz formula and linear matrix inequality(LMI) techniques, it was proved that a new stability condition of nonlinear neutral system with time-varying delays. When a solution to this set of LMIs exists, the parametric matrices can be easily obtained using LMI toolbox. Finally, numerical examples are given to illustrate the feasibility of the designed method.(3)The problem of robust H∞control for uncertain neutral systems with state time-delay and input time-delay is considered. Robust stabilization conditon is given for uncertain neutral systems with time-delay in term of integral inequality, combined with free weighting matrix and employed LMI techniques. Robust H∞ controllers and the methods of design of robust H∞controllers for a class of neutral systems with uncertainity and time-delay is obtained. The design of nomemory state feedback controllers for neutral systems with state delay and input delay such that the closed-loop system in asymptotically stable for all admissible uncertainty. Finally, numerical example is illustrated to show the use of obtained results.