# A nonlinear system

## Model description:

Consider a nonlinear system

\begin{align*} x_{1}(t+1) &=x_{1}(t)-x_{1}(t)x_{2}(t)+(5+x_{1}(t))u(t) \\ x_{2}(t+1) &=-x_{1}(t)-0.5x_{2}(t)+2x_{1}(t)u(t) \end{align*}

## Publication details:

 Title Stabilization of discrete-time nonlinear control systems - Multiple fuzzy Lyapunov function approach Publication Type Conference Paper Year of Publication 2009 Authors Kau, Shih-Wei, Huang Xin-Yuan, Shiu Sheng-Yu, and Fang Chun-Hsiung Conference Name International Conference on Information and Automation, 2009. ICIA '09. Date Published 06/2009 Publisher IEEE Conference Location Zhuhai, Macau ISBN Number 978-1-4244-3607-1 Accession Number 10837484 Keywords discrete time systems, fuzzy control, linear matrix inequalities, Lyapunov methods, nonlinear control systems, stability Abstract This paper deals with the stabilization problem for discrete-time nonlinear systems that are represented by the Takagi - Sugeno fuzzy model. By the multiple fuzzy Lyapunov function and the three-index algebraic combination technique, a new stabilization condition is developed. The condition is expressed in the form of linear matrix inequalities (LMIs) and proved to be less conservative than existing results in the literature. Finally, a truck-trailer system is given to illustrate the novelty of the proposed approach. DOI 10.1109/ICINFA.2009.5204890