Research On Event-triggered Control And Impulse Control Based On Piecewise Time-varying Lyapunov Functional Method

The periodic event-triggered control strategy is widely used in event-triggered control,due to its advantages of the reductions of the amount of data transmission,as well as being able to avoid the Zeno phenomenon.A possible weakness of this strategy is that the system information between ad-jacent sampling moments is ignored,which may lead to a drop in control performance.In order to improve the closed-loop performance of the system subject to event-triggered control,this thesis proposes a new type of ape-riodic event-triggered control strategy,which aims to provide the designer with a balance between closed-loop performance and reduced data transmis-sion by increasing parameter freedom of event conditions and implementing a so-called dual-stage periodic event detection scheme.It is worth pointed out that the closed-loop system under aperiodic event-triggered control is a class of state-dependent switching system with typical hybrid structure char-acteristics.On the other hand,the time-delayed impulsive system is another class of hybrid systems in which the states experience jumps at certain dis-crete instants.The delay-dependent stability problem for impulsive delay systems has not been fully solved due to their infinite-dimensional hybrid structures.For the aforementioned two classes of hybrid systems,this thesis develops piecewise time-varying Lyapunov functionals based analysis meth-ods in which the construction of Lyapunov functionals is related to the system structure.These methods can fully consider the coupling mechanism between the continuous and discrete dynamic of hybrid systems,and are able to pro-vide more accurate and effective ways to describe the influence of various system parameters on system stability and performance.Based on the pro-posed piecewise time-varying Lyapunov functionals based analysis methods,the aperiodic event-triggered control mechanism is designed,and the delay-dependent stability and the L2 gain criterion for the impulsive delay systems are established.The main results obtained in this thesis are formulated as follows:(1)An aperiodic event-triggered control strategy based on general quadrat-ic functions is proposed.The degree of freedom of the conventional even-t condition is increased by introducing a general quadratic function,and a piecewise time-varying Lyapunov functional is constructed in view of the characteristics of the switching structure of the closed-loop system.By em-ploying the matrix inequality techniques,the sufficient conditions for the ex-ponential stability of the closed-loop system and the finite L2 gain are es-tablished under the corresponding the event-trigger rule.Compared with the existing results,for given L2 gain performance level,the proposed method can effectively reduce the number of sampled-data transmission more.(2)A dual-stage periodic event-triggered output feedback sampled-data control strategy is proposed.On basis of the event-triggered mechanism anal-ysis,two period parameters h1 and h2 are introduced to strengthen the degree of freedom of the event-triggering rule,in which h1 denotes the sampling pe-riod,while h2 denotes the monitoring period.In the framework of the new event-triggered control,the closed-loop system is a switched system with multiple modes.The stability analysis is performed by applying switching time-varying Lyapunov functionals.Both the cases with/without network-induced delays are investigated.Based on a set of linear matrix inequali-ties(LMIs),the control mechanism of the proposed dual-stage periodic event-triggered strategy is established.The numerical simulation examples show that the proposed trigger control strategy can efficiently reduce the amount of data transmission while ensuring certain closed-loop stability performance.(3)For time-delayed impulsive systems,a piecewise time-varying dis-cretized Lyapunov functional analysis method is proposed.In order to avoid the complexity caused by the impulse-type Newton-Leibniz formula,a time-dependent complete Lyapunov functional is constructed.The time-varying weighting factor is introduced to coordinate the nondelayed term and the in-tegral term of the functional,which is quietly different from the complete Lyapunov functional for continuous time-delay systems.Further,by equidis-tantly partitioning the impulse interval and the time-delay interval,the dis-cretized form of the Lyapunov functional is obtained.Using this functional,combined with the use of a series of analysis techniques,the linear matrix inequalities-based sufficient conditions for exponential stability and finite L2 gain are derived.This method quantitatively reveals the influence of both time-delay intervals and impulse intervals on system performance.Numer-ical examples show that increasing the partition numbers on time-delay in-tervals and impulse intervals can significantly reduce the conservativeness of the results.