Abstract
This paper focuses on the problems of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation. First, a convex hull representation is used to describe the saturation characteristics. By constructing an appropriate copositive type Lyapunov functional, we give sufficient conditions for the existence of a state feedback controller such that the closed-loop system is positive and asymptotically stable at the origin of the state space with a domain of attraction. Then, the disturbance rejection performance analysis in the presence of actuator saturation is developed viaL1-gain. The design method is also extended to investigate the problem ofL1-gain analysis for uncertain positive systems with time-varying delays and actuator saturation. Finally, three examples are provided to demonstrate the effectiveness of the proposed method.
Highlights
Positive systems, whose states and outputs are nonnegative whenever the initial conditions and inputs are nonnegative, are of fundamental importance to multitudinous applications in areas such as economics, biology, sociology, and communications [1,2,3,4]
This paper focuses on the problems of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation
The linear copositive Lyapunov functional approach has been used to study the stability of positive systems due to the fact that it is less conservative than the traditional quadratic Lyapunov functional method [11]
Summary
Positive systems, whose states and outputs are nonnegative whenever the initial conditions and inputs are nonnegative, are of fundamental importance to multitudinous applications in areas such as economics, biology, sociology, and communications [1,2,3,4]. Some results on L1-gain analysis and control of positive systems have been reported in the literature [19, 22]. To the best of our knowledge, few results on positive systems with actuator saturation have been proposed [43, 44]. We focus our attention on the investigation of robust stabilization and disturbance rejection for a class of positive systems with time-varying delays and actuator saturation. By constructing a copositive type Lyapunov functional, a state-feedback controller design scheme is developed to guarantee the stability with L1-gain performance of the resulting closed-loop systems.
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