Stability Analysis For Uncertain Discrete-time Systems With Input Saturation

The input saturation is a kind of common nonlinearities. when the control inputs subject to the certain bounded constraints. The system are saturated. The performance of the system would be changed and the stability of the system would also be damaged. The problems of saturation increased a lot of difficulties not only to the design of engineering system, also to people’s life. In recent years, more and more scholars began to join the research of the stability of the input saturation system. It has an important significance to solve the effects of saturation in the control systems. The stability problem is investigated for discrete-time systems with input saturation In this thesis.Firstly, the stability problem is investigated for uncertain discrete-time system with input saturation. By using the Lyapunov stability theory and constructing the saturation-dependent Lyapunov function, the sufficient condition is given such that the system is asymptotically stable by combining the linear matrix inequality technique with the Schur lemma. Finally, a numerical example is given to demonstrate the effectiveness of the proposed method.Secondly, the stability problem is studied for the uncertain discrete-time systems with input saturation and state time-delay. To reduce the conservativeness of the stability criterion, the Lyapunov-Krasovskii function is constructed based on the Lyapunov-Krasovskii method. The stability criterion of the feedback control systems is derived by employing the linear matrix inequality (LMI) technique. Together with the matrix inequality, the sufficient condition is given such that the system is asymptotically stable and the robustly stable controller is designed. Numerical examples are presented to illustrate the feasibility and effectiveness of the controller design method.