Research On The Stability Of Two Types Of Sampled-data Stochastic Nonlinear Systems Based On Approximate Models

Continuous-time nonlinear systems are widely used in the modeling and analysis of practical systems,such as biological systems,physical circuits,economics,financial systems,and communication systems.At the same time,thanks to the rapid development of computer technology,more and more practical systems are controlled by computers or other digital devices.The control system with a digital controller and a continuous-time plant is the so-called sampled-data systems.Since the sampled-data nonlinear system can better describe the practical situation of the control system,it has received a lot of attention.stability analysis,an important subject of this kind of system,is gradually becoming a research hotspot.Indeed,most practical systems are affected by noise,which fails the stability analysis methods for general sampled-data nonlinear systems.Therefore,it is an urgent need to propose a stability analysis method considering noise characteristics to address this challenge.Note that Brownian motion and more general G-Brownian motion can better characterize the random properties of the noise in practical systems(especially financial systems).This thesis mainly considers two kinds of sampled-data stochastic nonlinear systems that driven by Brownian motion and G-Brownian motion,respectively,and proposes the stability analysis methods based on Euler-Maruyama approxi-mate discretetime model.The main research work of this thesis is as follows:(1)For a class of sampled-data stochastic nonlinear time-delay systems driven by Brownian motion,we first use the Euler-Maruyama method to construct the approximate discrete-time model for the system,analyze the one-step modeling error of the approximate discrete-time model in the mean square sense,i.e.,the one-step consis-tency condition,then study the closed-loop stability of the approximate system,and finally based on which,sufficient conditions of the mean square exponential stability for the original sampled-data closed-loop system are established.(2)For a class of sampled-data stochastic nonlinear systems driven by G-Brownian motion,by adopting the above approximation-based stability analysis method,we first construct an approximate discrete-time model according to Euler-Maruyama method,then analyze the multi-step modeling error between the approximate model and the accurate model of the system via setting a relatively small model calculation step,i.e.,the multi-step consistency condition,and finally develop,incorporating the relevant theory of G-expectation,the sufficient conditions of the mean square exponential stability for the original sampled-data closed-loop system on the basis of the stability of the approximate system.The correctness of our work has been verified through numerical simulation.