H_∞ Control For Nonlinear Discrete Singular Systems

With the expansion of the fields of system theory and the popularity and appliance of computer technology, discrete control systems have been developed quickly. Since nonlinear singular systems are more suitable to describe objective systems, it is necessary to research them. But there are few researches on these systems. This thesis studies H_∞ control for nonlinear discrete singular systems. The main contents and results in dissertation are as follows:(1)The problem of state feedback H_∞ control is explored for nonlinear discrete singular systems. By means of generalized Lyapunov function and Lyapunov equation, the stability is studied for the system. A sufficient condition is presented such that the system is zero solution asymptotically stable and a H_∞ norm constraint, based on which, a sufficient condition is given for the existence of a state feedback H_∞ controller, such that the resulting closed-loop system is zero solution asymptotically stable and a H_∞ norm constraint.(2)The output feedback H_∞ control problem is considered for nonlinear discrete singular systems. First of all, a sufficient condition is given such that the system is zero solution E - asymptotically stable and a H_∞ norm constraint. And the output feedback H_∞ controller is designed to guarantee the performance of the resulting closed-loop system.(3)We mainly concern the passive control problem for nonlinear discrete singular systems under bounded energy exogenous inputs and extend the definition of passivity to nonlinear discrete singular systems. Based on previous conclusion of stabilization, a sufficient condition is presented such that the system is zero solution asymptotically stable and passive. A sufficient condition is obtained for the existence of a state feedback passive controller, which makes the closed-loop system zero solution asymptotically stable and passive.(4)The H_∞ control problem is discussed for the nonlinear discrete singular systems with...