Exponentially Passive Control Problem For Singular Bilinear Systems

Singular bilinear systems have practical background and research value for accuratelydescribing the complex problems of physics, chemistry and economy. In recent years, alot of scholars research dissipative and passive problems for singular bilinear systems.This paper mainly researches exponentially passive control problems for singular bilinearsystems with multiple variable time delay and uncertainties. The main content of paperis as follows:(1)Firstly, singular bilinear systems and the problem of the passive control are intro-duced in this paper. At last, the main work of this paper is given.(2)Exponentially passive control problems for a class of singular bilinear system arediscussed. We design state feedback controller by constructing Lyapunove function andusing linear matrix inequality method, which guarantees the closed-loop systems to beadmissible and exponentially passive. Then the strictly exponentially passive controlproblem of singular bilinear systems with multiple Variable time delay and uncertainty isstudied by the same method. Finally, two numerical examples are given respectively totest the feasibility of the results.(3)We study exponentially passive control problem of a class of singular bilinearsystems based on state observer in this chapter. The paper designs observer which makesthe closed-loop systems to be exponentially passive. Therefore the su?cient conditionsare established in terms of linear matrix inequalities by introducing Lyapunove function.At last, we give a numerical example to test the feasibility of the result.(4)Summary of the main work is made.