| The systems in nature are always in a noisy environment and inevitably affected by various environmental noise s.Most researchers focus on the investigations of stochastic systems driven by white noises.Nevertheless,there are many kinds of environmental noises existing in practice,and stochastic systems cannot reasonably be used to describe all fluctuations occurring in nature.Hence,random systems driven by general noises appear.Besides,in view of the complexity and variability of the external environment,such as component breakdowns,failures or repairs and so on,many practical systems may experience abrupt changes in their parameters or structures.Continuous-time Markov chains can be used to model such abrupt changes.Generally,the systems driven by Markov chains are called Markovian switching systems which are essentially a class of dynamic hybrid systems.Considering hybrid and random factors together,this paper mainly focus on random coupled systems with Markovian switching,which is one of the more practical systems in hybrid stochastic systems.In fact,it is quite difficult for a system to realize self-stabilization because of the existence of Markovian switching and random perturbations.Adopting appropriate control scheme is one of the most effective methods to stabilize a system.This paper mainly investigates the global asymptotical stabilization in probability of random coupled systems with Markovian switching based on two types of discontinuous controls.On the one hand,intermittent control has been widely adopted in engineering fields,such as manufacturing,communication and transportation,due to the fact that it is easier to be implemented in engineering control.Compared with periodically intermittent control,the control width of aperiodically intermittent control is more general and flexible,since it does not require the periodicity of control interval.In the second chapter,the stabilization problem of random coupled systems with Markovian switching via aperiodically intermittent control is considered.On the basis of the Lyapunov method,graph theory together with some new stochastic analysis techniques,we present the Lyapunov-type criteria and the sufficient criteria related to coefficients of the systems.It is proved that the stability of the systems depends on control gain and the maximum proportion of rest time.Then the derived results are applied to random coupled oscillators models with Markovian switching,and the numerical simulations are given to illustrate the validity of the theoretical results.On the other hand,impulsive control,as a kind of discontinuous control,is much attractive because it has many advantages compared with continuous control,such as high reliability,maintenance with low cost,and high efficiency.In the third chapter,the stabilization problem of random coupled systems with Markovian switching via impulsive control is studied.Some sufficient criteria for the global asymptotical stabilization probability of the system with impulsive control are given.It is proved that the stability of the systems depends on the topological structure of the system,control gain,and average impulsive interval.Finally,a class of random impulsive coupled oscillators models are considered,and the numerical simulations are also presented to show the rationality of the results. |
