Research On Stability Of Positive Switched Linear Systems Based On Event-Triggered Control

A positive switched linear system is a special kind of hybrid system consisting of a finite number of continuous or discrete positive subsystems and a coordinated switching between positive subsystems.In practical applications,many special physical and chem-ical systems can be modeled and analyzed by the positive switched linear system due to the non-negative constraints on the system modes.Because the positive switched linear system combines the characteristics of both the switched system and the positive system,it is becoming a research hotspot to study the stability of positive switched linear systems.At present,there have been abundant achievements in theoretical research.In actual systems,sharing resources between systems can cause network congestion due to limited network bandwidth limitations.Therefore,in order to save the limited communication resources of the system and alleviate the pressure of data transmission bandwidth,event-triggered has a significant advantage in this respect compared with time-driven.Because each positive subsystem of positive switched linear system has different system performance,it is a research hotspot to use event-triggered control to efficiently configure the control resources of the positive switched linear system.As an important part of the positive switched linear system,the system needs to comprehensively consider the switching time and event-triggered time when performing the stability analysis of the positive switched linear system.Therefore,under the joint action of event-triggered control conditions and switching laws,it brings some challenges to the stability analysis of positive switched linear systems.The main research work of this paper is as follows:The stability of positive switched linear systems based on event-triggered control is studied.In order to solve the problem that the time-dependent switching rule wastes the limited resources of the system,we design the event-triggered switching condition based on state dependency.The event-triggered switching strategy has the following charac-teristics:(i)considering the event-triggered time combined with the switching time,the positive switched linear systems can determine the running order of each positive subsys-tem according to the current system performance.(ii)each positive subsystem has its own independent event-triggered condition.(iii)the designed event-triggered condition does not exhibit Zeno behavior.Based on the set theory and weak common linear copositive Lyapunov functions method,a sufficient condition for the continuous and discrete posi-tive switched linear systems to achieve asymptotic stability under external disturbances is established.The observer design and stability analysis of event-triggered control for positive switched linear systems are discussed.The event-triggered conditions based on the ob-served state are designed.Based on this,the key factor that positive switched closed-loop systems is positive is that the error is positive.A necessary condition for positive switched closed-loop systems to be positive and asymptotically stable is proposed by using linear programming.It is proved whether the positive switched linear system can perform pos-itive observer design.Under the state-based minimum switching strategy,the multiple Lyapunov functions method is used to establish a sufficient condition for the positive switched linear system with time-varying delay and external disturbance to have H_?per-formance.Finally,it is proved that the event-triggered conditions can exclude the Zeno behavior.Event-triggered design and stability analysis of positive switched linear systems un-der quantized transmission is considered.The state and input logarithmic quantization of positive switched linear systems with uncertainties are processed.Based on the peri-odically event-triggered sampled-data method,the multiple Lyapunov functions method and ADT switching strategy are used to establish a sufficient condition for the positive switched closed-loop system to achieve global exponential stability.At the same time,the maximal allowable number of successive packet losses is estimated while the system stability is satisfied.