Journal of South China University of Technology (Natural Science Edition) ›› 2015, Vol. 43 ›› Issue (1): 9-14.doi: 10.3969/j.issn.1000-565X.2015.01.002

• Electronics, Communication & Automation Technology • Previous Articles     Next Articles

Finite-Time Stability and Stabilization for a Class of Quadratic Discrete-Time Systems

Feng Zhi-hui1,2 Deng Fei-qi1 Liu Wen-hui1   

  1. 1. School of Automation Science and Engineering ，South China University of Technology ，Guangzhou 510640 ，Guangdong ， China ；2. Guangzhou Institute of Standardization ， Guangzhou 510050 ， Guangdong ， China
  • Received:2014-05-09 Revised:2014-11-12 Online:2015-01-25 Published:2014-12-01
  • Contact: 邓飞其（1962-），男，博士，教授，主要从事复杂系统研究 . E-mail:aufqdeng@scut.edu.cn
  • About author:冯智辉（1971-），男，博士生，高级工程师，主要从事标准化系统和标准化过程的建模、优化和控制研究 .E-mail ：feng-z-h@163.com
  • Supported by:
    Supported by the National Natural Science Foundation of China （ 61273126 ） and the Research Foundation for the Doctoral Program of Higher Education of China （ 20130172110027 ）

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Abstract: In practice ， finite-time stability of systems is more practical and economical than the traditional stability due to costs and other constraints. This paper studies the finite-time stability and stabilization for a class of quadratic discrete-time systems. By means of linear matrix inequality ， the design of feedback control gain matrix is converted into the solutions for linear matrix inequalities. Moreover ， sufficient conditions for the finite-time stability of closed-loop systems with state feedback are determined ， and a method to design the feedback control gain matrix is proposed to achieve the finite-time stability of systems. This method is also suitable to deal with the finite-time boundedness of systems with exogenous disturbance. Finally ， numerical examples are used for validation. The consistency of simulation and theoretical analysis results proves the feasibility of the proposed method.

Key words: quadratic discrete-time system, finite-time stability, state feedback, linear matrix inequality