Passive Control And Robust Control For Nonlinear Discrete Singular Systems

More than two decades, it was found that singular systems are more natural, more convenient and more accurate than normal systems to describe some actual systems. Since singular systems are widely applied to circuit, economy, machinery and other fields, and also can describe the actual systems appropriately, they get more attention. In addition, as we all know, many control systems have characteristics of nonlinearity. Strictly speaking, nonlinearity is a kind of common phenomenon, nonlinear systems are more suitable to describe objective systems, so it is necessary to research them. This paper mainly studies passive control and robust control for nonlinear discrete singular systems. The main contents and results in dissertation are as follows:(1) The problem of the passive control is explored for a class of nonlinear discrete singular system with allowed uncertainties under bounded energy exogenous inputs. The concept of’passive’is extended to this system for the first time. Under proper assumptions, by means of generalized Lyapunov function and linear matrix inequality, a sufficient condition is presented such that the system is zero solution asymptotically stable and passive, and the state feedback passive controller is designed to make the resulting closed-loop system zero solution asymptotically stable and passive.(2) The problem of the passive control is explored for a class of nonlinear discrete singular system with time-delay under bounded energy exogenous inputs. The concept of ’passive’ is extended to this system for the first time. Based on generalized Lyapunov function and stability theory, by means of linear matrix inequality and generalized algebraic Riccati inequality, a sufficient condition is presented such that the system is zero solution E-asymptotically stable and passive, based on which, the state feedback passive controller is designed to make the resulting closed-loop system zero solution E-asymptotically stable and passive. (3) The robust H∞control problem is discussed for a class of nonlinear discrete singular system with allowed uncertainties and time-delay. By means of generalized Lyapunov function and stability theory, the criterion of the system zero solution E-asymptotical stability is gained. Then, based on which, a sufficient condition is given such that the system studied is zero solution E-asymptotically stable and has H∞norm constraint, and the state feedback robust H∞controller is designed to guarantee the performance of the resulting closed-loop system.The examples are given correspondingly to prove the effectiveness of the conclusions gained.