Robust Control Of Linear Hybrid Systems With Parameter Uncertainties And Its Applications

Hybrid systems are composed of discrete event dynamic systems and continuous time dynamic systems or discrete time dynamic systems, which interact on each other.The hybrid system theory, which is proposed for the demand of the economic development, is the result of the development of computer science and control theory.Hybrid systems have very complex dynamic characteristics. The performance analysis and control of hybrid systems are difficult when the parameters perturb uncertainly. Therefore, it is necessary to propose the powerful approaches for robust performance analysis and control.Based on Lyapunov stability theory of hybrid systems and using the linear matrix inequality (LMI) method, this dissertation investigates the robust stability analysis problem, the robust stabilization problem and the robust performance synthesis problem for the linear hybrid systems with parameter uncertainties. The main contributions of this dissertation are as follows:(1)Using the LMJ method, the problem of robust stability is discussed for the uncertain continuous hybrid systems, of which the discrete event state transition conditions are state-dependant. Based on the common Lyapunov functions, the sufficient conditions are proposed for global robust asymptotic stability. Based on the piecewise quadratic Lyapunov functions, the sufficient conditions for local robust Lyapunov stability are derived.(2)The robust stability of uncertain linear discrete hybrid systems is investigated. The sufficient conditions for global robust asymptotic stability are proposed. Based on the multiple Lyapunov functions, the sufficient conditions are presented for local Lyapunov stability of general discrete hybrid systems. Using this result, the sufficient conditions are derived for local robust Lyapunov stability of the linear discrete hybrid sYstems with parameter perturbation.(3)The problem of robust stabilization for uncertain hybrid systems with multiple equilibria is considered. The sufficient conditions are derived for hybrid state feedback robust stabilization and hybrid dynamic output feedback robust stabilization, respectively. The design methods of the corresponding controllers are also proposed. The controllability or the observability of the continuous time subsystems is not required since the controllers consist of the discrete event dynamics as well as the continuous time dynamics.(4)The guaranteed cost control problem is studied for the uncertain impulsive hybrid systems and the integral quadratic cost functions. The synthesis approaches are introduced for guaranteed cost control laws via hybrid state feedback and hybrid dynamic output feedback. respectively. With the obtained control laws. the uncertainIvABSTRACTimpulsive hybrid systems can be robustly asymptotically stabilized and close loop costs are guaranteed. The guaranteed performance control problem is considered for the uncertain impulsive hybrid dynamic systems and the bounded amplitude performance objectives. The method is proposed for designing the guaranteed performance control laws via hybrid state feedback. With the guaranteed performance control laws, the uncertain impulsive hybrid systems can be robustly asymptotically stabilized and the amplitudes of the performance signals can also be limited to the given range.(5)The guaranteed performance control is applied to the vehicles with the automatic transmissions and the cruise controllers. With the guaranteed performance controller, the vehicle velocity stability and the ride comfort can be guaranteed under the uncertain conditions.