A Study On Asynchronously Switching Control Of Linear Switched Systems Based On Sampled Data

Switched system is an important hybrid system,which has been widely used in aeroengine system,constrained robot system and other practical engineering fields because of its modeling flexibility.Compared with the conventional system,the stability of the switched system not only depends on the characteristics of each subsystem,but also has a direct relationship with the switching signals.Therefore,the design of the controller and the switching rules should be considered in the study of the control problem of the switched system.In recent years,with the rapid development of computer technology and numerical control technology,the discrete feedback control based on sampled data has received more and more attention.But the existence of switching time series and sampling time series increases the complexity of the control design of switched system based on sampling data.Considering that the control feedback signals of the system can only be updated at the sampling point,when the activation time of the system is inconsistent with the sampling point,the delayed activation of the matching controller of the subsystem will inevitably cause the asynchronously switching control problem of the switched system,thus affecting the stability of the closedloop system.Based on the theory of multiple Lyapunov functions,this paper studies the asynchronously switching control problem of several classes of linear switched systems based on sampled data.The main contents are as follows:Firstly,for a class of linear neutral switched systems,a sampling control problem is investigated under asynchronous switching.By developing a novel edge-dependent discontinuous Lyapunov function approach,new exponential stability conditions are established for the considered switched system with sampled-data partitioned feedback controllers.In addition,the switching rules characterised by admissible edge-dependent average dwell time is first explored for sampling asynchronous switching studies of switched systems,and tighter bounds of admissible edge-dependent average dwell time are obtained by the edge-dependent discontinuous Lyapunov function strategy.By properly assigning the sampling period and the number of segments,the specific representation of the gain of the partition feedback controller corresponding to each subsystem can be obtained.Exact edge-dependent average dwell time improves the flexibility of system switching and reduces the conservability of the existing results.Two numerical examples demonstrate the effectiveness and superiority of the proposed method.Secondly,for the asynchronously switching sampling control problem of a class of linear switched systems with uncontrollable subsystems,a new aperiodic sampling mechanism satisfying the maximum asynchronous constraint and a partition-dependent discontinuous Lyapunov function control method based on sampling points are proposed.A sufficient condition for the global asymptotic stability of the closed-loop switched system is obtained by means of a switching rule which is superior to the traditional average dwell time.The proposed method not only the frequent switching is permitted in a sampling interval but also the partitioned Lyapunov function is allowed to increase in some segment of the synchronous operating period.The dynamic sampling rule with a maximum asynchronous running limit avoids high frequency switching of the sampled controller caused by frequent switching of subsystems,and further improves the control performance of the system.The partition control based on sampling points makes the synchronization running time and system switching times have a tighter boundary and makes the selection of switching signals more free.The effectiveness and feasibility of the proposed control method are verified by a numerical example.Finally,an output feedback trigger mechanism based on sampling points is proposed to solve the asynchronously switching control problem of a class of linear time-delay switched system.By means of the theory of multiple Lyapunov functions and the method of modeldependent average dwell time,the sufficient conditions for the exponential stability of the closed-loop switched system are given by the exponential observer.The proposed trigger mechanism further reduces the transmission of information and overcomes the limitation of network bandwidth.In addition,the trigger mechanism based on sampling avoids Zeno behavior which may exist in the simple event trigger control,and also enables the application of the output feedback control based on observer,which effectively solves the problem of system control when the state is unmeasurable.Simulation results verify the correctness and effectiveness of the proposed control method.