H_∞Control And Passive Control For Nonlinear Singular Systems

Singular systems are a class of the power systems which have more extensive forms than the normal systems. Singular systems extensively exist in many practical engineering systems, such as the power system, the electronic network system, the chemical reaction process and so on.H∞Control is the optimal control that the H∞norm of the transfer function between some signals in the system is used as the performance index. It has been applied to the traffic speed system, inverted pendulum, flexible arm, the attitude control of the spacecraft and so on.The passivity is the special case of the dissipation, the product of the output and the input is used as the rate of the energy in the passive control, and the attenuation characteristics of the system under the condition of the bounded input are reflected.H∞Control and passive control for the nonlinear singular systems are discussed in the article. The factors such as the cost of the implementing control and the reliance of the system are considered, it is feasible to select the control method of the output feedback. The paper is summarized as followed:(1) Passive control for a class of nonlinear discrete singular systems is discussed. By means of the generalized Lyapunov function, and a sufficient condition is given such that the nonlinear discrete singular system is passive and its zero solution is E-asymptotically stable, and based on it, a sufficient condition is presented such that the resulting closed-loop system is passive and its zero solution is E-asymptotically stable under the condition of the existence of a feedback passive controller, then the constructing method of the resulting controller is given. The validity of the design is proved with an example in the end.(2) The H∞output feedback control problem for the nonlinear secure singular system is discussed. By means of the generalized Lyapunov function, a sufficient condition is presented such that the zero solution of the nonlinear singular system is E-asymptotically stable. And based on it, a sufficient condition is given such that the resulting closed-loop system satisfies H∞norm constraint γ and its zero solution is E-asymptotically stable under the condition of the existence of output feedback controller. Moreover the constructing method of the resulting controller is provided. Finally a practical example is given to show the practicability of the design.