Stability Analysis And Control Synthesis Of Positive Systems

Positive systems have recently drawn researchers' great attentions due to their important applications in fields of ecology,communication engineering,economics,biomedicine and so on.This paper focuses on the stability analysis and control design problems for two main classes of positive systems which are switched positive systems and two-dimensional(2-D)positive systems.Based on the basic concepts and methods of the control theory,a series of well-established,systematical,and important results are obtained.As a whole,the main results of this dissertation are summarized in the following five parts.1.The problems of stability analysis,l1-gain performance analysis and state feedback controller design for discrete-time switched positive systems subject to actuator saturation are investigated.Based on the average dwell time approach and co-positive type Lyapunov function method,local exponential stabilization and weighted l1-gain performance analysis are studied,respectively.The state feedback controller design and the estimation on the domain of attraction are presented by solving a convex optimization problem.2.The problems of l1-gain performance analysis and control design for switched positive systems with dwell time constraint.The state-dependent switching satisfies a minimal dwell time constraint to avoid possible arbitrary fast switching.By constructing multiple linear co-positive Lyapunov functions,sufficient conditions of stability and L1-gain property are derived under the proposed switching strategy.Then,an effective state feedback controller is designed to guarantee the positivity and L1-gain property of the closed-loop system.3.The problems of finite-time stability and boundedness for continuous-time/discrete-time switched positive systems with time-varying delays under state-dependent switching are investigated.By utilizing co-positive type Lyapunov function method,sufficient conditions for solving the above-mentioned problems are derived.It is proved that the sliding motion caused by the state-dependent switching would not destroy the system performance.All the obtained results for continuous switched positive systems are extended to the discrete-time case.4.The problems of stability and positive observation for discrete-time two-dimensional positive systems with multiple delays described by Roesser model.Based on the concept of"oblique secant" and dual system theory,a novel proof is provided for the necessary and sufficient criteria of asymptotic stability proposed for the two-dimensional positive delayed systems.Based on the obtained stability criteria,necessary and sufficient conditions for the existence of two-dimensional positive observers.5.The problems of stability and constrained control for two-dimensional positive systems with multiple delays described in the second Fornasini-Marchesini model.Similarly,through applying the concept of "oblique secant and dual system theory,a novel proof is presented to establish necessary and sufficient conditions of asymptotic stability for the addressed systems.Then a state feedback controller is designed to ensure the non-negativity and stability of the closed-loop systems.Finally,a sufficient condition for the existence of constrained controllers is developed under the additional constraint of bounded control,which means that the control inputs and the states of the close-loop systems are bounded.Simulation examples have been provided for all prosed methods through this paper to illustrate the efficiency.