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This paper proposes a method to stabilize the origins of deterministic dynamical systems by state feedback control laws with Wiener processes. First, we obtain Ito-type stochastic dynamical systems by randomizing ordinary differential equation systems. Second, we design the diffusion coefficients. Then, we obtain Sontag-type global asymptotically stabilizers based on the stochastic control Lyapunov...
In this paper, we show discretized Lyapunov functions for various nonlinear dynamical systems by using the method that the authors have proposed. We use Kushner's scheme of difference approximation with directions and Alcaraz et al.'s quantization of Markov processes to approximate Lyapunov equations by linear Schroumldinger-like equations. We construct time-invariant functions concerned with the...
We propose a new procedure for designing approximate stochastic Lyapunov functions (SLFs) for nonlinear Ito stochastic systems. We approximate nonlinear stochastic Lyapunov equations (SLEs) by linear Schrodinger-like equations with Kushner??s scheme of difference approximation and Alcaraz et al.??s ??quantization of Markov processes.?? We construct time-invariant functions concerned with the solutions...
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