Passive Control For Bilinear Singular Systems

Bilinear singular systems is the nonlinear systems which is the closest to linear singular systems, it is closer to actual model than the linear singular systems. Many practical control engineering systems are the existence of time delay phenomenon. And the existence of time delay will cause instability and respond ability and performance deterioration of system, thereby greatly increasing the control difficulty. Moreover, it can be said that the passivity is a further abstraction of the stability. So it is very actually meaningful to study the passivity of bilinear singular systems with time delay.Firstly, the passive control problem for a class of bilinear singular system with time delay is discussed. The conception of passive is introduced into bilinear singular system with time delay. Based on the Lyapunov stability theory and by means of linear matrix inequalities (LMI), a sufficient condition is given for a class of bilinear singular time-delay systems to be asymptotically stable and passive. Moreover, we have designed a state feedback controller which guarantees stable and passive of the closed-loop systems. Finally, a numerical example is provided to illustrate the validity of the theorem.In addition, this paper presents the passive control problem for a class of uncertain bilinear singular systems with time delay. Designing a memory-less state feedback robust passive controller renders the bilinear singular system with time delay is singular quadratically stable and robust passive for all admissible norm-bounded parameter uncertainties. A sufficient condition for the memory-less state feedback robust passive controller of uncertain bilinear singular systems with time delay is derived by means of a linear matrix inequality(LMI) and Lyapunov function, and the explicit expression of the controller is derived in terms of the solution of LMIs. Finally, a numerical example demonstrates the validity and feasibility of the present approach.