Dynamic Analysis And Control For Several Classes Of Positive Systems

Positive system has played a very important role in many fields, since states of positive systems are defined on cones rather than in the whole space, it is a meaningful and challenging research on the dynamic properties of positive systems. Combining the problems appeared on the actual positive system, this dissertation will studies dynamic analysis and control for several classes of positive systems using positivity, specific contents are summarized as follows:Actuator saturation is one of the most common phenomenon existing in practical control systems since the capability of any physical actuator is limited, positive system is no exception. This type of problems is considered. This dissertation addresses the stability analysis and controller design, problems for a class of positive systems and interval positive systems in the presence of saturating actuators, gives several sufficient conditions for both the continuous-time and the discrete-time cases, respectively. Several sufficient conditions for stabilization and positivity are derived via the Lyapunov functions method and convex analysis, a state feedback control law is designed such that the closed-loop systems is asymptotically stable and the maximization problem of estimation of the domain of attraction are presented by solving a convex optimization problem with linear matrix inequalities (LMIs) constraints.This dissertation also investigates the robust reliable guaranteed cost control problem of positive interval systems with multiple time-delays and actuator failure, some critera for this type of controllers are derived for both the continuous-time and the discrete-time cases, respectively, a practical example is presented to illustrate the practicability and effectiveness of the results. A cost function is given, the actuator mold is adopted to describe variation of the actuators in the complete form, then, design a memoryless state feedback controller such that, for all admissible uncertainties as well as actuator failures occurring among the admissible subset of actuators, the closed-loop system remains asymptotically stable and possesses positivity, and the quadratic cost function has a certain bound, and then, the design problem of the optimal robust guaranteed cost controller is formulated as a convex optimization problem.Combined with the actual, this dissertation addresses the stability problem of switched positive linear systems with stable and unstable subsystems, propose some sufficient criteria of global uniform exponential stability for both the continuous-time and the discrete-time cases, respectively. Based on a multiple linear copositive Lyapunov function, and by using the average dwell time approach, some sufficient stability criteria of global uniform exponential stability are established, and points out how to choose parameters in practical application. All the theoretical results are proposed in terms of linear programming (LP), which can easily be solved.In practice, some dynamical positive system models are required to consider not only positivity but also impulsive effects, for example, the dynamic portfolio management and the integrated pest management system. This dissertation is concerned with the problems of stability for a class of impulsive positive systems. An impulsive positive system model is introduced and a necessary and sufficient condition guaranteeing the positivity of this kind of system is proposed, several sufficient criteria of stability, global exponential stability and global asymptotical stability for impulsive positive systems are established respectively by using a linear copositive Lyapunov. Additionally, this dissertation also studies the problem of exponential stability for a class of impulsive positive systems with mixed time-varying/constant delays. Two delayed impulsive positive system models are introduced and two necessary and sufficient conditions guaranteeing the positivity of two systems are proposed, respectively; by using copositive Lyapunov-Krasovskii functional and the average impulsive interval method, two sufficient criteria of global exponential stability are given for two delayed impulsive positive systems, respectively.Finally, a summary has been done for all discussions in the dissertation. The further and other works are presented for the problem of the positive systems.