Study On Problems Of Asynchronous Switching And Input-to-State Stability For Switched Delay Systems

Switched delay systems, as a special type of hybrid systems, have a wide range of practical background and important theoretical significance. The dynamical behaviors of switched delay systems are affected by the interaction among the continuous dynamic, the discrete dynamic, and the delay phenomenon, therefore, are very complicated. Many problems of analysis and syntheses need to be studied. This dissertation concerns the problem of asynchronous switching and input-to-state stability for switched delay sys-tems. The main contributions are as follows.Chapter 2 concerns the issue of H? control for a class of switched delay systems un-der asynchronous switching. The switching signal of the controller involves time delay, which results in the asynchronous switching between the candidate controllers and the systems. By combining Lyapunov-Krasovskii functional method with merging switching signal technique, H? state-feedback controllers are designed for the switched delay sys-tem under an average dwell time scheme. These conditions imply the relationship among the upper bound of the state delay, the switching delay and the average dwell time. Then, the control synthesis for a class of switched linear stochastic systems with time delays under asynchronous switching is considered.Chapter 3 investigates the stabilization problem for a class of switched neutral sys-tems under asynchronous switching. Time delays appear in both the state and the state derivatives. By using average dwell time method and Lyapunov-Krasovskii functional method, by further allowing the Lyapunov-Krasovskii functional to increase during the running time of the active subsystem with the mismatched controller, we provide suffi-cient condition in term of LMIs to guarantee the global uniform exponential stability of the closed-loop system under asynchronous switching, and then give the controller design.Chapter 4 concerns with analyzing input-to-state stability (ISS) for a class of switched nonlinear systems with time delays under asynchronous switching. When the subsystem is stabilized with the matched controller, the subsystem is ISS, otherwise the subsystem may not be ISS. By using dwell time method, we establish efficient condition, in terms of an upper bound on the switching delay, and in terms of a lower bound on the matched time intervals for the subsystem and the controller, which ensures ISS for the whole switched nonlinear system.Chapter 5 addresses the ISS of impulsive and switched nonlinear delay systems. Based on Lyapunov-Krasovskii functional method, we show that when only some of the constituent subsystems are ISS, the discrete dynamics are destabilizing, the ISS property still can be retained for the impulsive and switched nonlinear delay system, if the dwell time of the ISS subsystems satisfies a lower bound condition and the activation time of the non-ISS subsystems satisfies an upper bound condition, respectively. The proposed approach enables us to give the analysis of systems involving actuator failure, controller failure, or temporary uncertain switching signal.Chapter 6 concerns the construction of Lyapunov-Krasovskii functionals and input-to-state stability for switched nonlinear systems with input delay and disturbance. Without considering input delay and external disturbances, by using the pre-designed controller, the closed-loop system is exponential stability under the given average dwell time. In the presence of input delay and disturbance, under the switching signal for the switched nonlinear system without input delay, the system may not be ISS with respect to the disturbance. For this case, we establish some conditions to render the system admits a piecewise Lyapunov-Krasovskii functional, which is exactly constructed. Then, based the new Lyapunov-Krasovskii functional, if the switching signal satisfying the new average dwell time condition, the ISS property for the system can be guaranteed.Chapter 7 studies the construction of Lyapunov-Krasovskii functionals and input-to-state stability for switched nonlinear systems under asynchronous switching. It is assumed that the nominal system is exponential stability under a given switching signal satisfying average dwell time scheme. In the presence of switching delay, input delay and distur-bance, under this given switching signal, the system may not be ISS with respect to the disturbance. In addition, due to the existence of switching delay, the closed-loop system will experience asynchronous switching. For this case, we establish some conditions to render the system admits a piecewise Lyapunov-Krasovskii functional, which is exactly constructed. Then, based the new Lyapunov-Krasovskii functional, if the switching signal satisfying the new average dwell time condition, the ISS property for the system can be guaranteed.Finally, the results of the dissertation are summarized and further research topics are pointed out.