Stability Analysis And Output-Feedback Control Design Of Time-Delay Systems

The present paper focuses on the investigation of stability analysis and dynamics output-feedback stabilizing control design of time-delay Systems. The main contents of this paper are composed of the following parts:1. Stability Analysis of Time-Delay SystemsThe problems of stability of time-delay systems are studied. To begin with, as the preliminary knowledge of time-delay systems, the basic concepts of time-delay system stability are summarized, and sufficient conditions of stability of linear time-invariant systems with single delay in state are proposed. Then, based on the existing works, the problems of exponential stability of nonlinear time-varying delay systems with multiple delays in state are investigated. For these systems, the sufficient conditions of exponential stability are given in the form of Riccati Differential Equation and Lyapunov function, respectively. The upper bound of exponential convergent coefficients are obtained by introducing the concept of matrix measure. Finally, simulation results are addressed to illustrate the correctness of the proposed theoretical approach.2. Output Feedback Control Design of Time-Delay SystemsThe problems of dynamic output feedback stabilizing control design of time-delay Systems are investigated. With the existing works in hand, first, for linear state-delayed systems with single unknown delay in state whose upper bound is known, dynamic output feedback stabilizing controllers are developed. By Lyapunov-Krasovskii theorem, the sufficient conditions of exponential stability of closed-loop systems are proposed in the form of LMIs. Moreover, the above method mentioned is extended to investigate the dynamic output feedback stabilizing problems of the multiple state delays nonlinear systems whose nonlinearity satisfied Lipschitz condition and linear time-varying uncertain time-delay systems. The sufficient conditions which guarantee the exponential stability of closed-loop systems mentioned above are given in the form of LMIs. and the explicit form of exponential convergent laws are derived, respectively. Second, in order to overcome some of the inherent problems of the conventional Smith predictor method and provide better performance than memoryless controllers, Reduction method is introduced, i.e., the original system is transformed into a system without control input delay by variable transformations, dynamics output feedback controllers are proposed to stabilize linear systems with control input multiple delays and time-varying uncertain systems with con- trol input multiple delays respectively. Such controllers guarantee asymptotic stability of the closed-loop systems. The sufficient conditions of asymptotic stability of closed-loop system are proposed in the form of LMIs.3. Adaptive Output Feedback Control Design of Time-Delay Systems For the mistakes in the paper: "Stabilization of a chain of integrators with an unknown delay in the input by adaptive output feedback", IEEE Transactions on Automatic Control. 2006, 51(8): 1359-1363, some appropriate modifications are taken accordingly and thus a more rigorous proof is provided.