Hybrid dynamical systems, which consists of the discrete event system and continuous variable system, is a class of complex dynamical systems. The hybrid systems whose discrete event system is modeled as a finite state machine is considered in this thesis. Based on the multiple Lyapunov function method and the mode-dependent average dwell time technique and the theory of finite state machine, the exponential stability, the input-output finite time stability, the positive property, the hybrid observers and the iterative learning con-trol of hybrid systems are discussed in this thesis. The main works are summarized as follows:1. The asymptotic stability, the exponential stability and the stabilization of nonlinear impulsive hybrid systems based on finite state machine are studied. First, the definitions of asymptotic stability and the exponential stability are extended to this hybrid systems. Then, by constructing multiple Lyapunov function, the sufficient conditions of asymptotic stability, exponential stability are derived, and the feedback controller is designed to stabilize the hybrid systems exponentially. Due to the application of multiple Lyapunov function method and the mode-dependent average dwell time technique, the nonlinear term of only some subsystems of hybrid systems need to satisfy the global Lipschitz condition, therefore, the sufficient conditions of stability are weakened.2. The input-output finite time stability and the stabilization of nonlinear impulsive hybrid systems based on finite state machine are studied. First, the definition of input-output finite time stability is extended to such hybrid systems. Then, the stability of hybrid systems with two classes of exogenous input signals is discussed in the specified time interval, and the stability theorem are obtained. Finally, a state feedback controller is designed, and the sufficient condition of stabilization is given.3. The input-output finite time stability and the stabilization of time varying impulsive positive hybrid systems is studied. First, the sufficient condition of input-output finite time stability is proposed for the single linear time varying system, and the state feedback con-troller is designed to stabilized the non-autonomous system. Then, the sufficient conditions of input-output finite time stability for positive hybrid systems are derived and proved. Finally, in order to stabilized the non-autonomous hybrid systems, the output feedback controller is given.4. The observer problem is studied for the interval positive hybrid systems. First, the node observer is given, then, the observer for the continuous variable system of hybrid sys-tems is designed, based on the mode-dependent average dwell time technique, the sufficient condition of the exponential stability for the observe error systems is obtained. Finally, the feedback controller based on observer is proposed to stabilized the non-autonomous interval positive hybrid systems.5. The tracking problem of variable trajectories which are driven by deterministic fi-nite state machine (DFSM) is studied. First, the DFSM is repressed by a linear state equation with linear-inequalities, and the desired equilibrium set is defined for the DFSM. Then, a state feedback controller is designed to stabilized the DFSM at the desired equilibrium set. Finally, based on the prior results, a novel iterative learning control law and an initial state learning law are proposed for linear time varying system to track the variable trajectories driven by deterministic finite state machine, finally, a sufficient condition is obtained to ensure that the tracking error is convergent. |