A computing capability test for a switched system control design using the Haris-Rogers method

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• 作者：Mohd Amin AT-Tasneem ; Sallehuddin Mohamed Haris…
• 关键词：Linear inequalities ; Hybrid systems ; Stability ; Common quadratic Lyapunov function ; Numerical computation ; Symbolic computation ; TP273
• 刊名：Frontiers of Information Technology & Electronic Engineering
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：13
• 期：10
• 页码：781-792
• 全文大小：599 KB
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• 作者单位：Mohd Amin AT-Tasneem (1) (2)
  Sallehuddin Mohamed Haris (2)
  Zulkifli Mohd Nopiah (3)
  
  1. Faculty of Mechanical Engineering, University Malaysia Pahang, Pekan, 26600, Malaysia
  2. Department of Mechanical and Materials Engineering, Faculty of Engineering and the Built Environment, Universiti Kebangsaan Malaysia, UKM Bangi, 43600, Malaysia
  3. Unit of Fundamental Engineering Studies, Faculty of Engineering and the Built Environment, Universiti Kebangsaan Malaysia, UKM Bangi, 43600, Malaysia
  
• 刊物类别：Computer Science, general; Electrical Engineering; Computer Hardware; Computer Systems Organization
• 刊物主题：Computer Science, general; Electrical Engineering; Computer Hardware; Computer Systems Organization and Communication Networks; Electronics and Microelectronics, Instrumentation; Communications Engine
• 出版者：Zhejiang University Press
• ISSN：2095-9230

文摘

The problem of finding stabilizing controllers for switched systems is an area of much research interest as conventional concepts from continuous time and discrete event dynamics do not hold true for these systems. Many solutions have been proposed, most of which are based on finding the existence of a common Lyapunov function (CLF) or a multiple Lyapunov function (MLF) where the key is to formulate the problem into a set of linear matrix inequalities (LMIs). An alternative method for finding the existence of a CLF by solving two sets of linear inequalities (LIs) has previously been presented. This method is seen to be less computationally taxing compared to methods based on solving LMIs. To substantiate this, the computational ability of three numerical computational solvers, LMI solver, cvx, and Yalmip, as well as the symbolic computational program Maple were tested. A specific switched system comprising four second-order subsystems was used as a test case. From the obtained solutions, the validity of the controllers and the corresponding CLF was verified. It was found that all tested solvers were able to correctly solve the LIs. The issue of rounding-off error in numerical computation based software is discussed in detail. The test revealed that the guarantee of stability became uncertain when the rounding off was at a different decimal precision. The use of different external solvers led to the same conclusion in terms of the stability of switched systems. As a result, a shift from using a conventional numerical computation based program to using computer algebra is suggested. Key words Linear inequalities Hybrid systems Stability Common quadratic Lyapunov function Numerical computation Symbolic computation