Positive System Analysis And Controller Design Based On Finite-time Stability

With the development of control science and technology,many researchers find that there is a non-negative phenomenon in the control processes.That is,when the initial state and the control input of the system are positive,the corresponding state and control output are also positive or at least non-negative,which later is called the positive system.Actually,positive system is widely used in many fields,such as the biological systems,robotics,population system and sociology system.Industrial engineering,system control theory,social sciences are very widely used.Therefore,the research on the positive system is becoming a hotspot in the field of control system.On the other hand,when analyzing the stability of a system,many researchers always consider the Lyapunov asymptotic stability that reflects the steady-state performance of the system.However,in order to meet the actual engineering requirements,it should not only consider the asymptotic stability of the system,the transient performance of the system is also a factor that cannot be neglected.Since For the system's transient performance requirements,such as overshoot requirements,Dorato proposed the concept of finite-time stability(FTS)(also called as short time stability)in 1961.Subsequently,Weiss and other researchers also have given the concept of finite-time boundedness(FTB)in 1967.Since then,the finite-time stability theory has aroused the deep discussion and research in academia,and has appeared a lot of scientific research.As the research of the positive system is just starting,there are few systematic research results on the finite time stability analysis and design of the system.This paper analyzes and designs the finite-time control problem of positive system by using Lyapunov method and linear matrix inequalities(LMIs)technique.The main contents are as follows:(1)For a class of time-delayed and uncertain positive systems,an appropriate state feedback controller is designed such that the closed-loop system is positive and the finite-time bounded and meantime satisfies given H? performance index.(2)The finite time non-fragile control problem for a class of uncertain positive systems is discussed.It not only gives the sufficient conditions for the existence of the non fragile controller,but also the problem of controller gain solution is transformed into the problem of an optimal solution.The results are also applied to the circuit model.(3)For a class of positive systems with Lipschitz nonlinearities,the finite-time L2-L? control problem and sliding mode control problem are studied.By designing an appropriate controller,the closed-loop system is positive and the given performance indices are also satisfied.