Exponentially Dissipative Control Problem For Time-delay Systems

Dissipative problems and passive problems are the hotspot of research on control theory. The exponential dissipation of impulsive time delay system and exponentially passive is still very rare. The paper made some research about exponentially dissipative and passive control problems for time-delay systems and impulsive time-delay system.This paper focuses on the problems of exponentially dissipative control and exponentially passive control for time-delay system and the results will be summarized as follows:(1) The research background of the problem discussed in this paper is introduced. First of all, research background and current development situation of singular time-delay system and impulse time-delay system is introduced; Then, a brief introduction of the current situation and development prospects of the exponentially dissipative control and the exponentially passive are given; Finally, the main work is summarized.(2)The problems for differential impulsive time-delay system are discussed. Firstly, the general form of solution of the differential impulsive time delay system is transferred into the general form of solution of a differential pulse time-delay system. The sufficient conditions for the differential impulsive time-delay to be exponentially dissipative are given. And norm boundedness and inequality techniques are given to use to the proof.(3) We study the exponentially dissipative control problems of the singular time-delays system. The sufficient conditions are established in terms of linear matrix inequalities by introducing new Lyapunov-functions, which guarantees a singular time-delay system to be exponentially dissipative. Finally, for time-delay singular system we design state feedback controller and time-delay state feedback controller respectively, and the controllers make the closed-loop systems to be exponentially dissipative.(4) We study the exponentially dissipative control problem of the singular neutral time-delays system. Firstly, the sufficient conditions are established in terms of linear matrix inequalities by introducing new Lyapunov-functions, which guarantees a singular time-delay system to be exponentially dissipative.Finally, for singular time-delay neutral system we design state feedback controller and time-delay state feedback controller respectively, and the controllers make the closed-loop systems to be exponential dissipative.(5) We study the exponentially pativity control problem of the impulsive time-delays system. Firstly, the sufficient conditions are established in terms of linear matrix inequalities by introducing new Lyapunov-functions, which guarantees a singular time-delay system to be exponentially dissipative. We get the sufficient conditions for the exponentially pativity of the pulse points by using the method of inequality scale. The time-delay impulsive delay system is exponentially pativity.(6)Summary of the major work is made.