On the simultaneous stabilization of stochastic nonlinear systems

Abstract

Summary In this paper, the problem of simultaneous stabilization in probability by state feedback is investigated for a class of stochastic nonlinear systems whose drift and diffusion terms are dependent on the control and for which classical methods are not applicable. Under the assumption that a collection of stochastic control Lyapunov functions (SCLFs) is known and based on the generalized stochastic Lyapunov theorem, we derive sufficient conditions for the simultaneous stabilization in probability by a continuous state feedback controller that we explicitly compute. We also derive a necessary condition when the system coefficients satisfy some regularity conditions. This work generalizes previous results on the simultaneous stabilization of stochastic nonlinear systems. The obtained results are illustrated by a numerical example.

On state‐constrained porous‐media systems with gradient‐type multiplicative noise

“…7. In the case of nonlinear 𝛽, in order to design a stabilizing distributed control one may involve the simultaneous stabilization technique of stochastic nonlinear systems, see, for example, [22].…”

Finite‐time robust simultaneous stabilization control for two nonlinear singular time‐delay systems

“…In general, it is difficult to design a simultaneous stabilizing controller for nonlinear systems, so there are less works on the control design of simultaneous stabilization of nonlinear systems [5,6]. The author studied the problem of probabilistic simultaneous stabilization of a class of nonlinear systems via state feedback method [7]. In [8], based on generalized stochastic Lyapunov theorem and stochastic control Lyapunov function technique, a sufficient condition is obtained on the simultaneous stabilization of continuous single input nonlinear stochastic systems.…”

Event-Triggered Finite-Time <i>H</i><sub>∞</sub> Filtering for Discrete-Time Nonlinear Stochastic Systems

“…Based on the fundamental stochastic stability theory [1] and Lyapunov-Krasovskii functional [2], some results can be found in the literature [3]- [15]. Specifically, problems of stochastic stabilization and destabilization were studied for nonlinear differential equations by noise and impulsive stochastic nonlinear systems respectively in [4] [6] [10] [14]. References [5] [7] [11] [12] [15] investigated state-feedback and output feedback stabilization problems for stochastic nonlinear systems and stochastic delay nonlinear systems.…”