Stabilization by unbounded‐variation noises
Copyright policy )Stabilization by unbounded‐variation noises
SummaryIn this paper, we claim the availability of deterministic noises for stabilization of the origins of dynamical systems, provided that the noises have unbounded variations. To achieve the result, we first consider the system representations of rough systems based on rough path analysis; then, we provide the notion of asymptotic stability for rough systems to analyze the stability for the systems. In the procedure, we also confirm that the system representations include stochastic differential equations; we also found that asymptotic stability for rough systems is the same property as uniform almost sure asymptotic stability provided by Bardi and Cesaroni. After the discussion, we confirm that there is a case that deterministic noises are capable of making the origin become asymptotically stable for rough systems while stochastic noises do not achieve the same stabilization results. Copyright © 2016 John Wiley & Sons, Ltd.
- Kagoshima University Japan
Asymptotic stability in control theory, stabilization methods, stochastic systems, Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory, Systems and Control (eess.SY), stability analysis, nonlinear control systems, Electrical Engineering and Systems Science - Systems and Control, Stochastic ordinary differential equations (aspects of stochastic analysis), Optimization and Control (math.OC), Lyapunov stability, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Stochastic systems in control theory (general), Mathematics - Optimization and Control
Asymptotic stability in control theory, stabilization methods, stochastic systems, Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory, Systems and Control (eess.SY), stability analysis, nonlinear control systems, Electrical Engineering and Systems Science - Systems and Control, Stochastic ordinary differential equations (aspects of stochastic analysis), Optimization and Control (math.OC), Lyapunov stability, FOS: Electrical engineering, electronic engineering, information engineering, FOS: Mathematics, Stochastic systems in control theory (general), Mathematics - Optimization and Control
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