Study On Input-To-State Stability And Dynamic Output Feedback Control For Impulsive Systems

The instantaneously changed effect to the state are well described by impulsive differential systems, which are extensively applied in space technology, control system, biological systems, ecosystem and so on. In the mean time, impulsive systems can be seen as hybrid systems which are composed of continue-time subsystem and discrete-time subsystem, the problem of stability analysis and controller synthesis for impulsive systems is an important topic in automatic control. The existing research for impulsive systems focuses on the stability analysis without external disturb signal and the state feedback design with stable impulses. In the practical application, however, impulsive control systems are usually disturbed by the external signal, and the state may not be immediately measured, so it is needed to study on the ISS problem and dynamic output feedback problem for impulsive control. With the existence of the external signal, this paper considers the ISS analysis for the impulsive nearul network, dynamic output feedback H_∞controller design and H_∞filtering design for impulsive systems. The main work and research results of this thesis lie in the following.1. By using linear matrix inequality techniques, the ISS problem is considered for uncertain continue-time and discrete-time impulsive nearul network. Sufficient conditions with ISS property for the two typies of impulsive nearul network are developed on the condition of different sectors. Numerical examples are provided to demonstrate the effectiveness of the proposed design methods. 2. The design methods of dymanic output feedback H_∞control are provided for uncertain impulsive systems. Two types of impulses are considered: one is destabilizing, the other one is stabilizing. For each class of impulsive systems, sufficient conditions for robust stability and weighted limited L₂ gain are developed. Furthermore, based on linear matrix inequalities, sufficient conditions for the existence of dynamic output feedback H_∞controller are derived. Numerical examples and emulation figures are provided to demonstrate the effectiveness of the proposed design methods.3. The design approch with asymptotic stable linear H_∞filting is provided for the uncertain linear impulsive system with ecumenic form. Three types of impulsive systems are considered: on the condition of the zero external input, stable/stabilizable continuous-time dynamics / stabilizable discrete-time subsystem, unstable continuous-time dynamics / stabilizable discrete-time subsystem, stable/stabilizable continuous-time dynamics / unstabilizable discrete-time subsystem. For each class of impulsive systems, based on linear matrix inequalities, sufficient conditions for robust stability and weighted limited L₂/l₂ gain are developed from continuous-time input signal to continuous-time error signal and from discrete input signal to discrete error signal. Numerical examples are provided to demonstrate the effectiveness of the proposed design methods.