Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems

Abstract

This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.

Exponential Stability Analysis of Stochastic Semi-Linear Systems With Lèvy Noise

“…Moreover, most of the stability results are presented for SPDEs induced by Brownian motion. Brownian motion is a stochastic process with continuous paths, hence it could not be used to model stochastic disturbances in real-world systems like neurobiological systems, genetic regulatory models, singular systems and financial systems etc., [6], [14], [30], [41]. These systems are complicated in nature and have discontinuous paths, as a result the Brownian motion stochastic differential equation is falling to deal these issues.…”