随机系统的稳定性

Stability of the stochastic system

  • 摘要: 研究了随机系统d x(t) = [( A+ A(t)) x(t) + ( B+ B(t- τ1(t))) x(t- τ1(t))]dt+g(t,x(t) ,x(t- τ2(t)))d ω(t) 的指数稳定性,引入对应的确定性系统( 无不确定性、随机扰动与时滞) x·(t) = ( A+ B) x(t) 并设它是指数稳定的,应用Razumikhin 定理证明了当不确定性 A 与B、随机扰动g 及时滞τi(i= 1 ,2) 充分小时,原随机系统仍指数稳定.

     

    Abstract: Exponential stability of the stochastic system d x(t)=(A+A(t))x(t)+(B+B(t- τ 1(t)))x(t-τ 1(t)) d t+g(t,x(t),x(t-τ 2(t))) d ω(t) is investigated,and the corresponding deterministic system (without uncertainties,stochastic perturbation and delays) (t)=(A+B)x(t) which is exponential stable is introduced.By applying Razumikhin theorem,it is shown that the original stochastic system remains exponential stable provided that the uncertainties A,B ,stochastic perturbation g and delays τ ...

     

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