Research On Control Theory Of Periodic/Aperiodic Sampling Systems

Due to the different characteristics of the systems,such as non-minimum phase,hy-brid,time-delay,various types of troubles we need to deal with today are demanding prompt solution.For examples.high signal overshoot,extra synchronization error,and excessive cost to name a few.As a related topic and useful tool,sequence control is often used to suit its specific situation.As we could see.for a discrete-time non-minimum-phase system,when the sampling frequency is very high and the input is held at zero-order,the system has to face the increasing risk of instability.As a possible and feasible solution,the application of periodic control method simplifies the convergence analysis,while com-plexity could be reduced.For another example,considering about the rapidly developing complex dynamic network,since all the digital devices dominate the field of general sen-sors,the systems have to receive the signals only at discrete time instants as a consequence.Therefore,compared with the continuous time model,the sampling control technology has more influence and application potential in discrete-time communication pattern.More-over,unlike the periodic sampling method,aperiodic sampling control is more similar to keep path with natural systems,especially in practical applications.That is the reason that in discrete complex dynamic networks,the application of aperiodic sampling is consid-ered as a more interesting and challenging field.With the application on different scenes of periodic/aperiodic sampling.this paper focuses on the research of periodic control and ape-riodic sampling.trying to overcome some shortcomings of traditional methods.especially in discrete time non-minimum phase syste,ms,discrete-time complex dynamic networks with time-delayed.Improvements and extensions have been made.Through the research,following major results have been achieved:(1)In this paper,we present a direct multi-rate adaptive control algorithm that ensures global stabilization of a class of(potentially unstable and invertible)linear time-invariant discrete-time plants of known order and relative degree one.An essential feature of our scheme is that no projections are needed.no appeal is made to the persistence of excitation arguments for the stability proof and it has a better transient performance than existing schemes.The implementation of the controller requires some prior information about its Markov parameters,namely,upper and lower bounds on the systcems impulse response.It is directly applicable to plants with interlacing real poles and zeros.i.e.with Cauchy incdex equal to the plant order,provided the adaptation gain is restricted to be smaller than some value determined by the measure of relative primness of the pole and zero polynomial.Such that a class of practically and interesting systems satisfy Hermite-Hurwitz theory could be contained.Compared with current researches.better transient performance could be gained.(2)We present a new synchronization criterion in discrete-time communications for CDNs(complex dynamical networks)in this paper,which global exponential convergence is achieved.Between every two different nodes,the communications are discrete-time,at the same time between each two of the cormmunication instants.the intervals are time-varying and assumed to be bounded.We use time-dependent Lyapunov functional approach to give globally exponential conditions under the criterion tor synchronization of CDNs,with less conservatism and decision variables compared with some other existing results.such that the available information could be take full advantage of in the actual discrete-time communication pattern.Some simulations results are given at the end to show the effectiveness.(3)A new globally exponentially synchronization criterion CDNs(complex dy-namical networks)is proposed in this paper,with discrete time communications units and time delay is considered,in which globally exponential convergence is achieved.By in-troducing larger decision matrices to gain time-delay synchronization criterionit not only inherits the benefits that full utilization of available information,but also have less con-servatism.At the same time except for original system parameters,no more new decision variables are increased.A time-dependent Lyapunov functional approach is proposed to prove the effectiveness of the criterion.Some simulation results prove the feasibility of the theory.