Nonlinear Discrete-Time Singular Systems Subject To Actuator Saturation

Stability and Hx control of nonlinear discrete-time singular systems subject to actuator saturation are discussed in this paper, the nonlinear function satisfies a quadratic constraint. The nonlinear actuator saturation terms are transformed into Linear Matrix Inequalities (LMIs) by convex hull way, which are convenient to use Toolbox of Matlab. The state feedback controllers are designed for nonlinear discrete-time singular systems, which can make sure that the systems are regular, causal and stable.Chapter 1 introduces the research background and related conceptions as actuator saturation, singular systems, nonlinear systems, and the lemmas which will be used in later chapters.In Chapter 2, the stability for nonlinear discrete-time singular systems subject to actuator saturation is considered. A sufficient condition is acquired, which guarantees that the nonlinear discrete-time singular systems with actuator saturation are regular, causal, and stable. Then the condition is transformed into linear matrix inequalities by using Schur complement method, and the state feedback controller of nonlinear discrete-time singular systems subject to actuator saturation can be acquired by solving the LMI optimization problem.In Chapter 3, H∞ control for nonlinear discrete-time singular systems subject to actuator saturation is discussed. The H∞ state feedback controller is acquired to guarantee the systems are regular, causal, stable, and satisfy the H∞ performance.The conditions of theorems and controllers acquired in this paper are all LMIs expressed by original coefficient matrices given in the singular systems, there is no transformation for the singular systems, so it is convenient for solving by using Matlab.