## Model description:

Consider a nonlinear system

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

## Type:

## Form:

## Time domain:

## Linearity:

## 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 |