2020/04/01 by Shaosheng Zhou, Zhou, Shaosheng, Yingying Han +3
Business, Management and Accounting · Computer Science · Engineering · #Advanced Queuing Theory Analysis #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Stability and Control of Uncertain Systems #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2004.00194
openalex publication_date 2020/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper proposes a line integral Lyapunov function approach to stability analysis and stabilization for Itô stochastic T-S models. Unlike the deterministic case, stability analysis of this model needs the information of Hessian matrix of the line integral Lyapunov function which is related to partial derivatives of the basis functions. By introducing a new method to handle these partial derivatives and using the property of state-dependent matrix with rank one, the stability conditions of the underlying system can be established via a line integral Lyapunov function. These conditions obtained are more general than the ones which are based on quadratic Lyapunov functions. Based on the stability conditions, a controller is developed by cone complementarity linerization algorithm. A non-quadratic Lyapunov function approach is thus proposed for the stabilization problem of the Itô stochastic T-S models. It has been shown that the problem can be solved by optimizing sum of traces for a group of products of matrix variables with linear constraints. Numerical examples are given to illustrate the effectiveness of the proposed control scheme.