Stability Analysis Of Several Classes Of Stochastic Hybrid Systems And Its Applications In Networked Control Systems

Impulsive systems and switched systems are two important classes of hybrid systems.Impulsive systems include continuous-time dynamics and abrupt state jumps.Switched systems are composed of a family of subsystems and a switching signal.In practice,impulsive systems and switched systems are inevitably affected by random factors,such as the disturbance of stochastic noise on continuous dynamics,the randomly impulsive instants and jump intensity,the randomly switching time sequence,etc.In recent years,stochastic impulsive systems and stochastic switched systems have attracted considerable attentions and investigations of many researchers due to their extensive applications in the production and life.With the growing development and popularity of network technology,networked control systems are increasingly appearing in daily life and industrial engineering.Event-triggered control and impulsive control are widely applied in networked control systems because of their good control performance and efficient utilization of communication resources.Many practical systems are often disturbed by stochastic noises,the stochastic differential equation can correctly reflect natural properties and dynamic characteristics of these systems.This dissertation studies the stability analysis of randomly impulsive systems driven by Poisson processes and renewal processes,semi-Markovian switched singular stochastic systems and semi-Markovian switched systems with randomly impulsive jumps.On the basis of the modelling and analysis of stochastic hybrid systems,the design methods of event-triggered control strategy are proposed for networked control systems with stochastic noise.The main results of this dissertation are listed as follows:(1)The stability analysis of randomly impulsive systems driven by Poisson processes and renewal processes are investigated separately.For randomly impulsive systems with impulsive numbers obeying Poisson processes,the single jump map and multiple jump maps are discussed respectively.Using properties of Poisson process,sufficient conditions are proposed for the stochastic input-tostate stability and -th moment input-to-state stability.For randomly impulsive systems with impulsive numbers obeying renewal processes,multiple jump maps are driven by the discrete-time Markovian chain.By renewal theorem and ergodic theorem,the almost surely exponential stability is studied for considered systems.(2)The stability problem is investigated for semi-Markovian switched singular stochastic systems.The obtained results are applied to design controller for semi-Markovian switched stochastic systems with actuator saturation.The singular matrices with mode-dependent ranks are considered at the left-hand of semi-Markovian switched singular stochastic systems.An equivalent impulsive switched system is obtained by means of the mode-dependent coordinate transformation.And then,more general conditions for the existence and uniqueness of the solution are given together with a detailed expression of state jumps at switching instants.Using multiple Lyapunov functions method and stationary distribution of semi-Markovian process,sufficient conditions of almost surely exponential stability are presented for addressed systems.Applying stochastic Lyapunov functions method and transition rates of semi-Markovian process,sufficient conditions of stochastic stability and mean-square exponential stability are presented for considered systems.Then,based on results of stability analysis,the mode-dependent controller is designed for semi-Markovian switched stochastic systems with actuator saturation in the form of LMIs.Moreover,the domain of attraction in mean square sense is estimated.(3)For semi-Markovian switched stochastic systems with randomly impulsive jumps,the almost surely exponential stability is studied for cases that impulsive jumps and subsystems switches occur synchronously/asynchronously.For the synchronous case,the impulsive switching signal is modelled by a semiMarkovian process,which provides a unified framework for impulsive switched systems driven by Poisson processes,renewal processes or Markovian processes.For the asynchronous case,the randomly impulsive jumps are driven by a renewal process and a Markovian chain.Utilizing multiple Lyapunov functions method and stochastic process theory,sufficient conditions of almost surely exponential stability are obtained for addressed systems by comprehensively considering the effects of switches,impulses and stochastic noises on the system stability.(4)For the impulsive control problem of stochastic networked control systems,the time sequence and control gains of impulsive control are designed by the event-triggered control method.Both continuous and periodic event-triggered mechanisms,which do not rely on the expectation of system states,are designed for nonlinear stochastic systems.Sufficient conditions of the -th moment uniform stability and -th moment exponential stability are established for related systems.Especially,event-triggered parameters and impulsive control gains are specifically designed to guarantee the mean-square exponential stability of linear stochastic systems.For nonlinear stochastic systems modelled by T-S fuzzy models,the design scheme of event-triggered mechanism and T-S fuzzy controller is given to ensure stochastic finite-time stability in the terms of LMIs.(5)For stochastic networked control systems under cyber-attacks,mixed/Do S attacks are taken into account respectively and corresponding event-triggered control strategies are designed.For stochastic control systems under mixed attacks,event-triggered impulsive control strategies are designed with consideration of effects of randomly Do S attacks and randomly deception attacks.Based on continuous and periodic event-triggered mechanisms depending on the time,LMI conditions,which reveal the relationship among event-triggered mechanism,the probability and strength of cyber-attacks,and impulsive intensity,are established to ensure the mean-square exponential stability of addressed systems.For stochastic control systems under Do S attacks,event-triggered state feed-back control strategy is designed under constraints of average Do S duration and average Do S frequency.Based on the estimation of error state and current state and ACK mechanism,the switching event-triggered mechanism is designed.Sufficient conditions are given to ensure the stochastic input-to-state stability of considered systems under DoS attack.