Robust Stability Analysis And Control For Nonlinear Time Delay Systems

As we know that nonlinear systems exist in the world extensively, time delays are inherent in systems and uncertainties are not avoidable, so it is important to investigate the stability analysis and control of uncertain nonlinear systems with time delays. Now it is the hotspot and also the difficulty in control domain. Based on the existing literature, some work has been done in this paper on stability analysis and control of nonlinear time delay systems.In this paper, firstly absolute stability problem of uncertain Lurie time delay systems has been considered. By constructing special Lyapunov functions, We obtain sufficient conditions for the stability of systems dependent of the time delays and independent of the time delays respectively.Second, based on the sliding mode variable structure idea and adaptive fuzzy idea, this paper further considers variable structure adaptive fuzzy control for nonlinear time delay systems. The sliding mode is constructed dependent of the time delays, which can render the sliding motion exponentially stable. Then the robust adaptive feedback controllers are constructed, which can render the systems states reach the sliding mode in limited time. Therefore, the controllers will render the closed-loop systems asymptotically stable.This paper investigates two classes of nonlinear interconnected systems with time delays. Firstly, robust control problem for a class of interconnected system with nonlinear disturbances is considered, and output feedback controller is constructed to render the closed-loop systems asymptotically stable. Also a class of time varying nonlinear systems with time delays are considered with time varying delays and strong nonlinear sections in interconnections, for such systems a class of decentralized feedback controllers are constructed, which can render the closed-loop systems uniformly ultimately bounded stable.In the end, a class of nonlinear time delay chaotic systems are investigated, in which the time delay sections are not bounded by first-order polynomial, butbounded by high-order polynomial with unknown gains. For such systems, two classes of feedback controllers are proposed, which are both independent of time delays and can render the closed-loop systems stable in the sense of uniform ultimate boundedness. Compared with the existing resuts, the results of this paper are more applicable, and we consider the uncertain case, so the results are more general.