Stability Analysis And Attraction Domain Estimation Of Two Classes Of Discrete Time Positive Linear Systems

Positive systems are widespread in many fields and play an extremely important role in them.Because the state space of the positive system is defined on the cone within the non-negative quadrant,however the state space of the general system is defined in the whole linear space.Therefore,the comprehensive study of positive system is more complex than the general system.According to the particularity of the positive system,the positive discrete system with control constraint and actuator saturation constraint is considered in this paper.The stability analysis and the estimation of the attractive domain are studied.The following are the main research contents of this paper:The research content of this paper is divided into five chapters.On the basis of the existing research on positive system,the stability analysis,state feedback controller design and the estimation of attraction domain of positive system are further studied.This paper mainly discusses the control synthesis of positive discrete linear systems with control constraints and positively discrete linear systems with actuator saturation constraints.The first chapter mainly describes the research status of positive system at domestic and overseas.The importance of the control constraint and the actuator saturation constraint are introduced respectively.Furthermore,it lists the main research contents and innovation points.The second chapter of this paper mainly introduces some basic knowledge to prepare for the future research content.The basic concepts of positive system,saturated system,domain of attractive,convex set and convex hull are given.Based on the above basic concepts,the stability analysis of the closed-loop system,the design of the controller,the estimation of domain of attraction and the treatment of the saturation link are introduced.The main research contents of the third chapter are:The stability analysis and the estimation of the attractive domain are studied for positive discrete linear systems with control constraints.The research idea is based on the stability criterion condition of the unconstrained positive discrete system.The condition of stability criterion with control constraints is obtained and the state feedback controller is designed for the closed-loop system.Then,the contraction invariant ellipsoid set of the quadratic Lyapunov function is introduced to estimate the attraction domain of the corresponding closed-loop system.The maximum attraction domain estimation is obtained by designing a convex optimization problem with linear matrix inequality formal constraints and with the objective function of maximizing the ellipsoid volume.The feasibility of the method is verified by numerical experiments.The main research contents of the fourth chapter are:The stability analysis and the estimation of the attractor domain for positive discrete time linear systems with actuator saturation constraints are studied.The idea is to treat the positively discrete linear saturated system with saturation constraint by convex hull representation.Then,by solving the problem of linear equations,the stability criterion of the closed-loop system with saturation constraint is obtained,and a state feedback controller is designed for it.The quadratic Lyapunov function level set,which can be used as the asymptotically stable domain of the system,is used to estimate the system attraction domain.The maximization of the attraction domain is obtained by maximizing the volume of the ellipsoid by designing a convex optimization problem with a formal constraint of linear matrix inequality.And the feasibility of the method through simulation result.Finally,a summary has been done.The further and other woks are presented for the problem of the positive systems.