Variable structure control of stochastic systems with colored noises in terms of practical stability (Q2744495)

The authors study the continuous-time stochastic systems \(\dot x(t)=Ax(t)+ Bu(t)+F(t)+\eta(t) G(t)\), where all parameters or variables are of suitable dimensions, \(\eta(t)\) is an Ornstein-Uhlenbeck process, \(B\) \((\in \mathbb{R}^{n\times m})\) is of full rank with respect to columns and there exists an \(n\times n\) nonsingular matrix \(T\) such that \(TB=[OI_m]^T\), and \((A,B)\) is controllable. The closed-loop systems for \(x(t)\) under the variable structure control law are then designed. The achievability, practical stability and robustness of the sliding mode are proved. A simulation example shows the good effectiveness of the proposed method.