New Polynomial Lyapunov Functional Approach to Observer-Based Control for Polynomial Fuzzy Systems with Time Delay

作者：Ammar Imen Iben; Gassara Hamdi; El Hajjaji Ahmed; Chaabane Mohamed

来源：International Journal of Fuzzy Systems, 2018, 20(4): 1057-1068.

DOI：10.1007/s40815-017-0425-8

• Polynomial fuzzy systems
• Polynomial fuzzy observer
• Line-integral polynomial Lyapunov function
• Dual system
• Sum Of Squares
• SOSTOOLS

This paper presents a new Line-integral polynomial Lyapunov functional approach for observer-based control for a class of polynomial fuzzy systems with time delay and unmeasured state variables. To guarantee the global asymptotic stability and estimation error convergence, a design method is proposed. In this work we consider a Line-integral polynomial Lyapunov function in which the Lyapunov matrices are polynomial matrices depending not only of the estimated states but also of the estimated delayed states and we use the dual system to reduce the computational efforts. The design conditions are established in terms of Sum Of Squares (SOS) which can be numerically and symbolically solved via the recent developed SOSTOOLS and a Semi-Definite Program solver. Finally, numerical examples are proposed to show the validity and applicability of the proposed results .

• 出版日期2018-4