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Stability and stabilization of homogeneous stochastic systems

This study considers homogeneous stochastic systems and shows their stability and stabilization. We define a homogeneous stochastic system as an extension of a homogeneous deterministic system. We show that homogeneous systems can exhibit exponential stability or finite-time stability according to the degree of homogeneity. Further, we show a control law for the stabilization of homogeneous stochastic control systems. Numerical examples of stable homogeneous systems and the stabilization of a homogeneous control system are also presented.