On the Asymptotically Stability with Respect to Probability via Stochastic Matrix-valued Lyapunov Systems
Keywords:Stability, Asymptotically, Lyapunov matrix-valued function. Stochastic probability, control systems
In this paper, we study the stability to system in Kats-KrasovskiiÂ Â form, in terms of the stochastic Matrix-valued function. Ï€(t,x,y) constructedÂ for system dx/dt = f(t,x,y(t) ) x(t0 )=x 0,y(t0 )=y0 and use the Lyapunov matrix-valuedÂ function to established the necessary and sufficient conditions that guarantees the asymptotically stability of the control systems.
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