Event-triggered Control Of Positive Switched Systems

In practice,many control systems can be modeled via positive systems,whose states are always non-negative.Positive switched systems are a special kind of hybrid systems,which are composed of positive subsystem and a switching law.Such systems can describe various practical systems such as queuing systems,air traffic systems,HIV treatment processes in medical systems,and so on.In most existing systems,the controller design is always based on timetriggered sample.This control strategy requires the systems state to be updated at each sampling time instant.It may lead to the waste of system resources and increase the design cost.Considering these problems,a novel control strategy called event-triggered control is introduced.It can reduce the conservativeness of time-triggered control.Up to now,there have been many results on the event-triggered control of general(non-positive)switched systems.However,few results are developed for the event-triggered control of positive switched systems.It will also cause the waste of resources and increase design costs if the time-triggered control strategy is used for investigating the control synthesis of positive switched systems.Based on these points,the event-triggered control of positive switched systems is proposed in this thesis using linear programming and a matrix decomposition technology.The average dwell time switching of the systems is designed by linear copositive Lyapunov functions.The details are as follows:Chapter 1 is the Introduction.First,the research background and significance of the thesis are described.Then,the research status of positive systems and positive switched systems is summarized.Furthermore,the current research status of input saturation,time-delay and eventtriggered control is introduced.Finally,the main research contents are summarized.Chapter 2 investigates the event-triggered control of positive switched systems.First,a 1-norm based event-triggered control strategy is established.Then,some sufficient conditions for the stability of systems are obtained by means of linear copositive Lyapunov functions.The gain matrices of the controller and cone attraction domain are designed by the matrix decomposition and linear programming approach.Furthermore,an improve event-triggering condition is presented and the controller gain is designed.The Zeno behaviour can be avoided under the designed control law.Finally,the proposed design approach is extended to continuous-time positive switched systems.Compared with existing results,the designed event-triggered controller can reduce the sampling frequency and save resources.Chapter 3 proposes the event-triggered L1 control of nonlinear positive switched systems.Assume that the nonlinear function is located in a sector.First,an event-triggering condition is established for the systems.By virtue of the event-triggering strategy,the original system is transformed into an interval uncertain system.Then,an event-triggered L1-gain controller is designed by decomposing the controller gain matrix into the sum of nonnegative and non-positive components.All presented conditions are solvable in terms of the linear programming.Finally,the maximum attraction domain is estimated by means of the linear programming approach.Chapter 4 considers the event-triggered control of positive switched systems with randomly occurring saturation and time delay,where actuator saturation and time delay obey different Bernoulli distributions.First,under the presented event-triggering condition,the eventtriggered controller and the cone domain gain matrices are designed based on the matrix decomposition technology.A linear copositive Lyapunov-Krasovskii functional is constructed for the systems.The positivity and the stability of the system are achieved by considering the lower and the upper bound of the system,respectively.By means of the linear programming approach,the maximum attraction domain is estimated.Finally,the obtained approaches are extended to interval and polytopic uncertain systems,respectively.Chapter 5 summarizes the main content of the thesis and proposes some future research topics.