The Research Of Stability Of Control Systems With Saturation Constraints

Nonlinear constraints exist in control systems generally, saturated nonlinearity is one of the most common nonlinear constraints. The performance of control systems subject to saturated nonlinear constraints can be seriously influenced, what's more, it can make the system unstable. Therefore, it is necessary to research the stability of saturated control systems, and has important theoretical and practical significance. In this paper, stability analysis of control systems both in the presence of actuator saturation and under state saturation are discussed, the remainder of this paper is organized as follows:1. The problem of practical stabilization of control systems in the presence of actuator saturation and input additive disturbance is studied. Aiming at the three dimensional control systems subject to saturation under some assumptions, according to the conditions that state matrix satisfies, the practical stability of the systems are discussed in eight scenarios. First, according to the status of actuator saturation, three dimensional space can be divided into three regions, and then during the certification process, saturation is replaced by convex combination, last by use of some matrix algebraic Riccati equation, the tendency of the system's trajectories are detailed analyzed under various circumstances of the state matrices. By adjusting the value of the parameter of the control law above, five in the eight cases of the closed-loop system can be global or semi-global practical stabilization, while in other cases the closed-loop system can not be global or semi-global practical stabilization when the saturation presents.2. The problem of global stabilization of control systems subject to actuator saturation and input additive uncertain disturbance is discussed. First under certain assumptions, the problem to be solved is proposed, and then the method to design a new low-high gain state feedback control law by some matrix algebraic Riccati equation is given. By adjusting the value of the parameter of the control law above, the problem proposed can be solved, namely, when the uncertain disturbance exists, the closed-loop system can be global practical stabilization by the low-high gain state feedback control law; and if the disturbance does not exist, the closed-loop system is globally asymptotically stable.3. The problem of global asymptotic stability of control systems under state saturation is discussed. Under the assumption that the system matrix is Hurwitz stable, consider a class of three dimensional autonomy systems in the canonical form subject to state saturation. First, the global asymptotic stability of equilibrium point is studied respectively on the basis of the saturated case of every component of the state, combined the conditions in each case, the sufficient condition for global asymptotic stability of the control system based on the matrices of the solution of Lyapunov equation is obtained. Subsequently, the tendency of the system's trajectory is discussed according to the derivative of the state on the boundary of its definition domain, and the sufficient condition based on the parameters of the system matrix is obtained to make the system globally asymptotically stable.