A new result on stabilization analysis for stochastic nonlinear affine systems via Gamidov’s inequality

Abstract

The Lyapunov approach is one of the most effective and efficient methods for the investigation of the stability of stochastic systems. Several authors analyzed the stability and stabilization of stochastic differential equations via Lyapunov techniques. Nevertheless, few results are concerned with the stability of stochastic systems based on the knowledge of the solution of the system explicitly. The originality of our work is to investigate the problem of stabilization of stochastic perturbed control-bilinear systems based on the explicit solution of the system by using the integral inequalities of the Gronwall type in particular Gamidov's inequality. Namely, under some restrictions on the perturbed term, and based on the method of integral inequalities, we prove that the stochastic system can be stabilized by constant feedback. Further, we study the problem of stabilization of stochastic perturbed control affine systems based on the use of bilinear approximation. Different examples are provided to verify the effectiveness of the proposed results.

Stability analysis of time–varying perturbed descriptor systems

“…The practical stability only needs to stabilize a system into a region of phase space, namely the system may oscillate close to the state, in which the performance is still acceptable. In the past decades, practical stability has been studied by many researchers such as cited in [4,5,6,7,13]. The concept of "practical stability" means that the origin is not an equilibrium point and the convergence of the system state is towards a ball.…”