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Front. Inform. Technol. Electron. Eng.  2012, Vol. 13 Issue (10): 781-792    DOI: 10.1631/jzus.C1200074
    
A computing capability test for a switched system control design using the Haris-Rogers method
Mohd Amin At-Tasneem, Sallehuddin Mohamed Haris, Zulkifli Mohd Nopiah
Faculty of Mechanical Engineering, University Malaysia Pahang, Pekan 26600, Malaysia; Department of Mechanical and Materials Engineering, Faculty of Engineering and the Built Environment, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Malaysia; Unit of Fundamental Engineering Studies, Faculty of Engineering and the Built Environment, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Malaysia
A computing capability test for a switched system control design using the Haris-Rogers method
Mohd Amin At-Tasneem, Sallehuddin Mohamed Haris, Zulkifli Mohd Nopiah
Faculty of Mechanical Engineering, University Malaysia Pahang, Pekan 26600, Malaysia; Department of Mechanical and Materials Engineering, Faculty of Engineering and the Built Environment, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Malaysia; Unit of Fundamental Engineering Studies, Faculty of Engineering and the Built Environment, Universiti Kebangsaan Malaysia, UKM Bangi 43600, Malaysia
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摘要： 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.
关键词： Linear inequalities;  Hybrid systems;  Stability;  Common quadratic Lyapunov function;  Numerical computation;  Symbolic computation    
Abstract: 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
收稿日期: 2012-03-19 出版日期: 2012-10-01
CLC:  TP273  
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Mohd Amin At-Tasneem
Sallehuddin Mohamed Haris
Zulkifli Mohd Nopiah

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Mohd Amin At-Tasneem, Sallehuddin Mohamed Haris, Zulkifli Mohd Nopiah. A computing capability test for a switched system control design using the Haris-Rogers method. Front. Inform. Technol. Electron. Eng., 2012, 13(10): 781-792.

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