| Positive systems is a kind of system whose state values are always non-negative.Switched positive systems are based on positive systems theory and consist of several positive subsystems and a switching signal that determines the switch of each subsystem.In most existing systems,the signal sampling mechanism is often based on time-triggered sampling mechanisms.Compared with time-triggered sampling mechanisms,event-triggered sampling mechanisms can reduce the sampling frequency,thus achieving resource conservation.In practical applications of switched systems,unstable subsystems often occur due to interference,unmodeled dynamics,and possible faults.The presence of unstable subsystems has been proven to inevitably affect the stability and performance of the control systems.On the other hand,filter and observer in switched positive systems play an important role in control theory and engineering practice.By designing filters and observers,system states and output signals can be extracted and estimated,thus achieving control and monitoring of the systems.In switched positive systems,filter and observer can also be used to deal with the impact of unstable subsystems,ensuring the stability of the entire systems.Therefore,it is of great significance to conduct research on event-triggered filter and observer in switched positive systems with unstable subsystems.This paper mainly focuses on the filter and observer problems of switched positive systems with unstable subsystems,and the specific content is as follows:(1)Based on event-triggered mechanism,an event-triggered filter is designed for a switched positive systems with unstable subsystems.Firstly,a static event-triggered framework is established.Then,the gain matrix of the event-triggered filter is designed using matrix decomposition algorithm.Next,the filter error system is constructed.Lastly,by using linear co-positive Lyapunov function method and linear programming algorithm,the conditions for ensuring positivity and stability of the system are obtained,and the design problem of the event-triggered filter for the switched positive systems with unstable subsystems is solved.(2)By extending the technique of disturbance observer,a disturbance observer is designed to estimate the disturbance from an external system,and the estimated disturbance is applied to the design of the filter.Next,based on the event-triggered mechanism,the gain matrices of both the disturbance observer and the filter are designed using matrix decomposition technique.Finally,the conditions for ensuring positivity and stability of the system are obtained by using linear co-positive Lyapunov function method and linear programming algorithm,thus solving the asymptotic filter design problem for the switched positive systems with unstable subsystems.(3)By introducing a dynamic variable,the static event-triggered mechanism is improved to an adaptive event-triggered mechanism.Then,an adaptive triggering framework is proposed and an adaptive event-triggered parameter update condition more suitable for positive systems is designed.The gain matrix of the observer is designed using matrix decomposition algorithm,and the observer error system is constructed.Finally,the conditions for ensuring positivity and stability of the system are obtained by using Lyapunov function and linear programming algorithm,thus solving the design problem of the adaptive event-triggered observer for the switched positive systems with unstable subsystems. |
