Saturation Control Of Several Switched Linear Systems

Actuator saturation is an inevitable phenomenon in real physical system recently. It has been highlighted and investigated by many researchers. Switching systems exist widely in engineering systems, such as communication systems, mechanical systems and automotive industry. A lot of researches in this direction have been done in the last decades. For an input saturation system, a restricted input may not be able to stabilize the corresponding system. So, in the second part, we research exponential stability of singularly perturbed switched systems subject to actuator saturation with stabilizable and unstabilizable subsystems. In recent years, with the development of science and technology, it is more and more common that computers are used to control some devices of the actual systems. The input signal of the computer system is discrete-time. As we know, the continuous-time system is controlled by the controller with discrete-time signal in sampled-data control systems, such as computer system. Many techniques have been proposed in some literature to deal with the sampled-data control systems. However, the problems of stability of switching sampled-data control systems with actuator saturation are still open. So we consider the problem of exponential stabilization for a class of sampled-data control switched systems subject to actuator saturation in the third part. Similarly with the discrete-time controller in sampled-data control systems, all information of the sampling system are discrete-time. Furthermore, fast sampling is necessary and valuable in control systems. But systems tend to become ill conditioned. Delta operator can effectively deal with this problem due to its excellent performance in finite-word-length computers under fast sampling. So we consider the robust state feedback stabilization problem of uncertain delta operator switched linear systems subject to actuator saturation in the forth part of our paper. The main contributions are as follows:The problem of exponential stabilization for a class of singularly perturbed switched systems subjected to actuator saturation is considered. Based on the time-dependent switching signals and multiple Lyapunov functions method depending on the singular perturbation parameter, exponential stabilization conditions in terms of LMIs are established and a basin of attraction depending on the singular perturbation parameter is constructed too.A novel Lyapunov function is defined, whose derivative is negative along the trajectories of the continuous-time model of the sampled-data control system. It is shown that this fact guarantees that a quadratic Lyapunov function is strictly decreasing for the discrete-time system. Improved LMI conditions are constructed, which can be cast in optimization problems aiming at enlarging estimate of the region of attraction of the closed-loop system.We address the robust stabilization problem for a class of switched delta operator systems with actuator saturation. The objective is to design a robust controller to stabilize the uncertain delta operator switched system by using multiple Lyapunov functions and to design minimum dwell-time switching rule and state switching rule respectively. By using the multiple Lyapunov functions method, sufficient conditions for robust exponential stabilization at the origin with a larger attractive region are derived.