Global stability and stabilization of more general stochastic nonlinear systems

Global stabilization via time-varying output-feedback for stochastic nonlinear systems with unknown growth rate

“…This assumption shows the presence of serious parameter unknowns and hence system (1) essentially differs from those in [13][14][15] where the growth rates of the systems investigated therein are precisely known though the nonlinearity of the systems in [14,15] is stronger than that of system (1). Assumption 2 shows that the control coefficient of system (1) is unknown but belongs to a known interval.…”

“…With the measured output dependent growth, output-feedback control design has been investigated in [8][9][10][11] for classes of stochastic strict-feedback nonlinear systems. The subsequent development focuses on the more heavy nonlinearities in the stochastic nonlinear systems [13][14][15]. Specifically, [13] gives an output-feedback control design for the stochastic nonlinear systems with linear unmeasured states dependent growth, and [14] considers the output-feedback stabilization for the high-order stochastic nonlinear systems with homogeneous unmeasured states dependent growth.…”

“…Specifically, [13] gives an output-feedback control design for the stochastic nonlinear systems with linear unmeasured states dependent growth, and [14] considers the output-feedback stabilization for the high-order stochastic nonlinear systems with homogeneous unmeasured states dependent growth. In the setting of weak solutions, by generalizing the concepts of stochastic stability and establishing corresponding criterion theorems, our recent work [15] provides a more general and powerful framework of stochastic stability and stabilization, and with the help of which, the results in [13,14] have been essentially extended, that is, the Lipschitz conditions on the drift and diffusion terms and the strong restriction on the degree of homogeneity are not necessary any more for the output-feedback stabilization of stochastic nonlinear systems.…”

Adaptive state feedback control for switched stochastic high‐order nonlinear systems under arbitrary switchings

“…Proof Since f k ( t , x ) and are piecewise continuous in t and continuous in x for k ∈ M , f σ( t ) ( t , x ) and are piecewise continuous in t and continuous in x for t ≥0. Under Assumption and from “Definition ” in the work of Li and Liu, system has a continuous local solution x ( t ) on for any initial data, where is the explosion time satisfying . We therefore need only to show that almost surely.…”

Robust Stability, Stabilization, andH∞Control of a Class of Nonlinear Discrete Time Stochastic Systems

“…∞ control is one of the most important robust control approaches, which aims to design the controller to restrain the external disturbance below a given level. We refer the reader to [4][5][6][7][8][9] for stability and stabilization of Itô-type stochastic systems and [10][11][12][13][14] for stability and stabilization of discrete time stochastic systems. Stochastic ∞ control of Itô-type systems starts from [15], which has been extensively studied in recent years; see [16][17][18][19][20] and the references therein.…”