Stability Analysis And Impulsive Control Of Switched Positive Systems

Switched positive systems are composed of a finite number of positive subsystems and a switching mechanism,which combines the unique non-negative characteristics of positive systems with the complex dynamic behavior induced by switching laws,so the research of such systems is more challenging than positive systems and switched systems.Existing research on switched positive systems has made some progress,but it has mainly focused on switched positive linear time-invariant systems,and there are still many unresolved issues.Furthermore,actual positive systems often exhibit impulse characteristics due to external environmental interference or human intervention,which further increases the dynamic complexity of positive systems.Meanwhile,impulsive control,as a simple and efficient non-continuous control strategy,has solved many problems that continuous control systems cannot solve,and has been widely used in various fields,thus attracting the attention of researchers.However,most current impulsive control methods are aimed at single systems,and there is little research on the more complex and widely applicable switched positive systems.In view of this,this dissertation presents an in-depth study of the stability analysis,state bounding estimation and impulsive control problems of switched positive systems based on DT method and impulse system theory,which further enriches and develops the relevant conclusions of switched positive systems.Specifically,the main research contents are as follows:(1)Stability analysis methods based on ADT and minimum DT switching strategies are proposed for discrete-time switched positive linear time-varying systems.By constructing a class of indefinite discrete time-varying Lyapunov functions,a sufficient condition is established to ensure stability of system,which effectively reduced the conservatism of traditional research methods.Additionally,based on the possible state convergence behavior of subsystems in a fixed interval,an improved function-dependent bounded DT switching method is proposed,which solve the stability problem of the system containing unstable subsystems.(2)The stability,impulsive perturbation and impulsive control problems of switched positive nonlinear systems with partially unstable subsystems and degrees of homogeneity one are investigated.Firstly,sufficient conditions for guaranteeing exponential stability of impulse-free switched positive nonlinear systems is proposed by means of the multiple MSLF technique and ADT switching.On this basis,considering the influence of asynchronous impulses on system performance,the mode-dependent average impulsive interval condition is introduced to inscribe impulse frequency and various impulsive effect are analyzed.Then,exponential stability criteria for impulsive switched positive nonlinear systems is derived,which solves the problem that the complex dynamic behaviour caused by the interaction of switching topology and asynchronous impulses is difficult to analyse.Finally,a mode-dependent event-triggered impulsive control scheme that can effectively avoid the Zeno behaviour is designed by using impulsive control theory,which ensures that the resulting system is positive and globally asymptotically stable.(3)Two types of initial state-dependent DT switching schemes are proposed for the finite-time state bounding problem for switched positive nonlinear systems with unknown external interference and degree less than one.By making full use of the homogeneity and cooperativity of vector fields,and combining mathematical induction with multiple MSLFs,some sufficient conditions to ensure that the state trajectory of the system can converge to a bounded region within finite time under any non-negative initial conditions are derived,which overcomes the disadvantages that traditional DT switching cannot guarantee the existence of the state boundary of the system.Meanwhile,the above results are extended to general Persidskii-type switched systems by applying the comparison principle.(4)The finite-time stability problems for two classes of switched positive nonlinear systems with mixed homogeneous degrees are investigated.First,a finite-time stability analysis method based on the bounded DT switching strategy is proposed for the first time for switched positive nonlinear systems,where the degrees of subsystems are not all the same,and are either equal to one or less than one.By strictly restraining the total activation time of subsystems with degree of homogeneity one,the lower bound on minimum DT that guarantees the finite-time stability of such system and estimates of the corresponding convergence time are derived using mathematical induction and multiple MSLFs.Secondly,a positive impulsive controller design method based on maximum DT switching is proposed for a class of switched positive nonlinear systems with subsystems composed of nonlinear terms having different homogeneous degrees,and the global finite-time stability criterion of the system is given,which effectively solves the stabilization problem of the system containing unstable homogeneous terms.