Tracking Control Of Switched Linear Systems With Time-Delays

As an important class of hybrid systems, switched time-delays systems are of great significance both in theory development and engineering applications. Due to the co-existence and interaction among the continuous dynamics, discrete dynamics and time-delays, the behavior of such systems is very complicated. The mechanism of such systems is far from clear. Many analysis and design problems deserve further investigation. As one of the basic problems in control theory and engineering, tracking control of switched time-delays systems has broad applications in navigation, spaceflight, robot control and networked control systems. However, up to now results on such issues have been rarely found.This dissertation studies tracking control of switched linear systems with time-delays based on stability analysis and control synthesis of switched systems and time-delays systems. Some theories and methods of tracking control are applied and extended to establish a theory framework of tracking control for switched linear time-delays systems. By using convex optimization techniques, single Lyapunov functions, multiple Lyapunov functions and average dwell time methods, the dissertation studies the tracking control problems for the cases that the systems are with uncertainties, perturbations, and have stabilizable and unstabilizable subsystems, respectively. Meanwhile, the tracking control problems for switched time-delays systems are addressed for the output tracking control and the tracking control with H∞model reference tracking performance, respectively.The main contributions of this thesis are as follows.1. State tracking control for switched linear time-delay systems is studied with de-lay independent sufficient conditions given for the case that the delay is constant. By using convex optimization techniques and single Lyapunov function method, tracking controllers and a hysteresis switching law are designed such that the H∞model reference tracking performance is guaranteed.2. Average dwell time approach is utilized to design robust tracking controllers and switching law for the switched linear systems with time-varying delays, and sufficient conditions for the solvability of robust tracking control problem are developed such that the weighted H∞model reference robust tracking performance is satisfied. Free weight- ing matrix scheme and a specific Lyapunov-Krasovskii functional are adopted to obtain the delay dependent criteria which are less conservative. The constrained conditions are reduced and simplified compared with existing results, and thus the difficulties and com-plexities are reduced.3. When the system states are not available, observer based tracking control for switched linear systems with time-delays is considered. The possibility of designing switching control law based on measured output instead of the state information is in-vestigated to achieve H∞model reference tracking performance. In order to overcome the difficulties caused by the estimation error and exotic disturbance, the variation-of-constants formula is adopted. Delay independent and delay dependent criteria are given for the cases that the system is with constant delay and time-varying delays, respectively. The simulation examples show the effectiveness of the proposed method.4. Robust tracking control is addressed for a class of switched time-delay systems with uncertainties that satisfy certain matching conditions. Since the reference models are still time-delay systems, the variation-of-constants formula is introduced to estimate the reference states. Asymptotic tracking is achieved by means of exponential stability of the error system.5. For the switched time-delays systems with stabilizable and unstabilizable sub-systems, the tracking control problem is solvable if the activation time ratio between sta-bilizable subsystems and unstabilizable subsystems is no less than a specified constant. To this end, average dwell time approach is extended to the switching tracking control design, and "PI" (proportional-integral) controllers are adopted to the design which atten-tively eliminates the steady state tracking error.Finally, the results of the dissertation are summarized and further research topics are pointed out.