Robust Dissipative Control For Bilinear Descriptor Systems

Dissipative theory was brought forward by Willems in 1970s,which plays an important role in the stability research of systems. Its essential implication is that finding a nonnegative energy function such that the supply rate of the energy is always less than the energy consumption of systems.Bilinear descriptor system is a kind of nonlinear descriptor system which is most close to the linear descriptor system. Moreover, it is closer to actual model than the linear descriptor systems and widely exists in the practical lives. In actual control systems, delay and uncertainty are pervasive for various reasons which are the two major factors lead to the control system instability. Therefore, it is very practically meaningful to research the dissipative control problem of bilinear descriptor systems. According to the problem of delay and uncertainty for bilinear descriptor system, the robust dissipative control for bilinear descriptor system has been studied by using the linear matrix inequality (LMI) method.Firstly, the robust dissipative control problem of time-delay bilinear descriptor systems with dissipative uncertainties is researched in the paper. The conception of dissipative uncertainties is introduced into bilinear descriptor systems. Based on the Lyapunov stability theory and by means of linear matrix inequality (LMI), a sufficient condition is given for time-delay bilinear descriptor systems with uncertainties to be robust stable and strictly dissipative. Moreover, we have designed a state feedback controller which guarantees the robust stable and strictly dissipative. A numerical example demonstrates the validity and feasibility of the proposed method.In addition, this paper has discussed the problem of observer-based robust dissipative control for uncertain bilinear descriptor systems with time-varying delay. The conception of dissipativity is introduced into bilinear descriptor systems. An observer-based controller is designed such that the?closed-loop systems is robust stable and strictly dissipative for all admissible uncertainties. And the corresponding observer and controller are constructed by solving the linear matrix inequality. Finally, a numerical example is provided to illustrate the validity of the means.Finally, the problem of elastic robust dissipative control for uncertain bilinear descriptor systems is researched. Bysolving the linear matrix inequality(LMI), the elastic state feedback controller which can guarantee the closed-loop system is robust stable and strictly dissipative has been designed. Simulation results show the accuracy of the method.