Research On Event-triggered Control Of Positive Markov Switching System

In the past decades,positive systems have aroused great interest owing to its strong practical application ability.As an important class of dynamical systems,positive systems have a unique property: the states and outputs are always non-negative for non-negative initial conditions and inputs.Positive Markovian switching systems can not only effectively describe the dynamic process with Markov parameters,but also have strong modeling ability for special Markov switched systems with positive constraints.Therefore,positive Markovian switching systems have gradually become a hot topic in the field of control.In this paper,an eventtriggered controller is designed for positive Markovian switching systems,which can save limited network resources on the premise of achieving stability of the controlled system.The main work of this paper can be summarized as follows:The finite-time control problem is investigated for discrete-time positive systems subject to event-triggered scheme and Markovian switching parameters.Firstly,on the basis of the1 norm,a developed event-triggered scheme is proposed to be associated with the error signal and the state signal.Furthermore,a linear co-positive Lyapunov function and an average dwell time approach are adopted to obtain sufficient conditions for guaranteeing stochastic finite-time stability of the underlying systems.Then,a matrix decomposition strategy is constructed to design a finite-time event-triggered control law such that the corresponding Markovian switching systems are positive and stochastically finite-time bounded.All conditions are proposed on the basis of linear programming.Finally,a local railway transportation model is provided to verify the practicability of the strategy.The problem of event-triggered control is investigated for discrete-time positive Markovian switching models subject to actuator faults and deception attacks.Firstly,a Bernoulli distribution is adopted to depict random deception attacks.Considering the positivity of Markovian switching models,an event-triggered control is constructed based on a 1 norm.Next,in order to handle actuator faults and random deception attacks,exponentially stochastic stability conditions are established by developing a linear co-positive Lyapunov function approach.Furthermore,a non-fragile control law combined with the event-triggered control is proposed such that exponential stochastic stability of the corresponding system is achieved on the basis of matrix decomposition strategy and linear programming.Finally,a data communication network model is provided to demonstrate the effectiveness of the proposed controller.The problem of adaptive event-triggered control is investigated for continuous-time positive semi-Markov jump models in the presence of deception attacks.Firstly,a Bernoulli distribution is presented to characterize the random deception attacks.To save the limited network resources,an adaptive event-triggered mechanism is constructed,in which the communication threshold can be dynamically tuned according to the error and state signals.Next,on the basis of linear co-positive Lyapunov function and gain matrix decomposition,stochastic stability conditions are developed under the framework of deception attacks.Then,the positivity and stochastic stability of the underlying system are guaranteed in linear programming.Furthermore,by means of a lower bound of inter execution time,the occurrence of the Zeno phenomenon will be avoided.Finally,a urban water system model is shown to verify the proposed theoretical findings.