Control Synthesis Of Switched Positive Systems With Asynchronous Switching

Switched positive systems,composed of a set of positive systems together with a law to orchestrate the switching between them,trigger extensive interest of scholars in control community because of numerous practical applications of such systems,such as networks congestion control and population dynamics and the like.Some results on stability analysis and control synthesis for switched positive systems have been proposed.Nowadays,the related results of control synthesis for switched positive systems are mostly based on a common assumption that the switching instants of controllers coincide with those of system modes.Nonetheless,the switching signal of controllers is mismatched with the subsystems for the reason including detection delay or false alarm in practical control systems.In other words,the asynchronous switching phenomenon is inevitable.In this paper,the asynchronous switching problem resulting from detection delay and the extended asynchronous switching problem caused by detection delay and false alarm are mainly discussed as follows:The controller design issue for a class of impulsive switched positive systems under asynchronous switching in continuous-time context is addressed.The state-feedback controller is designed to guarantee the positivity and exponential stability for the underlying system by means of multiple linear copositive Lyapunov functions approach and dual system theory incorporated with linear programming problem.The switching signal satisfies an average dwell time and the total running interval ratio between normal working period and detection delay period is restricted to be more than a known constant.Finally,the validity of our main results is demonstrated by a simulation example.The controller design problem for a family of discrete-time switched positive systems with networked time delays is first discussed.An event-triggered scheme is adopted,which can reduce communication resources and save the cost.By utilizing the nonnegative property of system,a mode-dependent linear triggering condition is proposed,which is more efficient to address the positive stabilization problem.With the aid of a copositive type LyapunovKrasovskii functional and the average dwell time approaches,the asynchronously eventtriggered state-feedback controller is designed to guarantee the positivity and exponential stability for the closed-loop system.Finally,a simulation example is exploited to verify the validity of the proposed theoretical results.An extended asynchronous switching control issue for a family of switched positive systems is investigated for the first time.By resorting to a novel set of switching signals superior to the average dwell time switching,the state-feedback controller is designed to guarantee the resulting closed-loop system to be positive and asymptotically stable.Unlike the existing results,the obtained results allow the Lyapunov function to increase in the switching delay period,false alarm period,unstabilizable subsystems running period and all switching instants,which is less conservative.A numerical example with practical considerations is used to show the effectiveness and potential of the proposed theories.In addition,an extended asynchronous switching control problem where the number of the false alarms is allowed to be no more than is analyzed.Based on the dual system theory,sufficient condition of the existence of the designed controller is given to guarantee the positivity and exponential stability for the closed-loop system.Finally,a numerical example is presented to demonstrate the validity of our results.