Observer-based controller design for a class of switched positive systems with interval uncertainties and time-varying delays is studied.
For a class of uncertain switched time-delay positive systems, an observer-based controller is designed to guarantee the positive constraints of the augmented system by using the theory of Metzler matrix and non-negative matrix.
At the same time, the exponential stability of the augmented system under the average dwell time switching signal is obtained by constructing a multi-Lyapunov function. Switched systems are a class of important hybrid systems, which are composed of a group of continuous or discrete subsystems and switching rules. Switching system has a wide application background in power system, Constrained Robot system, intelligent highway and other systems. In recent years, it has attracted wide attention at home and abroad [2]. On the other hand, some physical quantities, such as population, absolute temperature and material density, can only be positive or negative. Taking these physical quantities as the state variables of the system, thermostatic element the concept of positive system is obtained.
Positive system is a kind of system: for any non-negative initial condition, the state trajectory of the system remains non-negative.
In the past ten years, more and more studies have been done on positive systems.
If every subsystem in the switched system is a positive system, it is called a switched positive system. Due to the non-negative limitation of switched positive system state, the results obtained by many general switched systems can not be directly applied to switched positive systems. Therefore, although many results have been obtained in switched systems and positive systems in recent decades, the study of switched positive systems is still very necessary. In the actual system operation process, time delay is ubiquitous, and it is the main cause of system instability and performance degradation.
At present, time-delay switched positive systems have been extensively studied and many important results have been achieved.
In practical systems, uncertainties and delays may arise due to various unavoidable factors, such as modeling errors, system operating environment changes, measurement errors and information transmission delays.
Therefore, the study of uncertain time-delay switched systems has important practical value and theoretical significance. This paper considers a class of switched positive systems with parameter uncertainties and time-varying delays, and studies the observer-based controller design problem.
The observer-based controller is designed to guarantee the positive requirement of the augmented system. Meanwhile, the exponential stability of the augmented system under the switching signal of average dwell time is obtained by constructing multiple Lyapunov functions. Based on the linear matrix inequality (LMI) method, a sufficient condition for the augmented system to be positive and exponentially stable is given.