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

doi:10.1631/jzus.C1200074

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

Computer & Automation | Updated：2022-05-19

- A computing capability test for a switched system control design using the Haris-Rogers method
- A computing capability test for a switched system control design using the Haris-Rogers method
- Frontiers of Information Technology & Electronic Engineering Vol. 13, Issue 10, Pages: 781-792(2012)
- Affiliations：
  
  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
- Author bio：
  
  [ "Mohd Amin AT-TASNEEM, E-mail: tasneem@ump.edu.my" ]
  Sallehuddin Mohamed HARIS, E-mail: salleh@eng.ukm.my
  [ "Zulkifli Mohd NOPIAH, E-mail: zmn@eng.ukm.my" ]
- Funds：
- DOI：10.1631/jzus.C1200074
  CLC： TP273
- Received：19 March 2012，
  
  Revised：2012-;9-11，
  
  Published：2012-10
- Accepted：
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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[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(10): 781-792.
DOI：

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[J]. Frontiers of Information Technology & Electronic Engineering, 2012, 13(10): 781-792. DOI： 10.1631/jzus.C1200074.

摘要

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.

关键词

Keywords

references

G. Davrazos , , , N.T. Koussoulas . . A General Methodology for Stability Analysis of Differential Petri Nets . . 10th Mediterranean Conf. on Control and Automation , , 2002 . . p.296 - - 302 . . . .

R.A. Decarlo , , , M.S. Branicky , , , S. Pettersson , , , B. Lennartson . . Perspectives and results on the stability and stabilizability of hybrid systems . . Proc. IEEE , , 2000 . . 88 ( ( 7 ): ): 1069 - - 1082 . . DOI: 10.1109/5.871309 http://doi.org/10.1109/5.871309 . .

Z. Geng . . Switched Stability Design on Canonical Forms . . Int. Conf. on Information and Automation , , 2010 . . p.289 - - 293 . . . .

M. Grant , , , S. Boyd . . Cvx Users' Guide for Cvx Version 1.21 . . 2012 . . .

S.M. Haris . . Analysis and Design of Classes of Hybrid Control Systems . . PhD Thesis, University of Southampton, UK , , 2006 . . .

S.M. Haris , , , E. Rogers . . A Matlab Toolbox for Finding Stabilizing Controllers for a Class of Switched Systems . . Int. Conf. on Computational Intelligence for Modelling Control & Automation , , 2008 . . p.238 - - 242 . . DOI: 10.1109/CIMCA.2008.115 http://doi.org/10.1109/CIMCA.2008.115 . .

S.M. Haris , , , M.H.M. Saad , , , E. Rogers . . A Method for Determining Stabilizability of a Class of Switched System . . 7th WSEAS Int. Conf. on Systems Theory and Scientific Computation , , 2007 . . p.27 - - 32 . . . .

J.P. Hespanha , , , A.S. Morse . . Switching between stabilizing controllers . . Automatica , , 2002 . . 38 ( ( 11 ): ): 1905 - - 1917 . . DOI: 10.1016/S0005-1098(02)00139-5 http://doi.org/10.1016/S0005-1098(02)00139-5 . .

C. King , , , R. Shorten . . Singularity conditions for the non-existence of a common quadratic Lyapunov function for pairs of third order linear time invariant dynamic systems . . Linear Algebra Its Appl. , , 2006 . . 413 ( ( 1 ): ): 24 - - 35 . . DOI: 10.1016/j.laa.2005.07.023 http://doi.org/10.1016/j.laa.2005.07.023 . .

D. Liberzon , , , J.P. Hespanha , , , A.S. Morse . . Stability of switched systems:a Lie-algebraic condition . . Syst. Control Lett. , , 1999 . . 37 ( ( 3 ): ): 117 - - 122 . . DOI: 10.1016/S0167-6911(99)00012-2 http://doi.org/10.1016/S0167-6911(99)00012-2 . .

O. Mason , , , R. Shorten . . A Conjecture on the Existence of Common Quadratic Lyapunov Functions for Positive Linear Systems . . American Control Conf. , , 2003 . . p.4469 - - 4470 . . . .

V.F. Montagner , , , V.J.S. Leite , , , R.C.L.F. Oliveira , , , P.L.D. Peres . . State feedback control of switched linear systems:an LMI approach . . J. Comput. Appl. Math. , , 2006 . . 194 ( ( 2 ): ): 192 - - 206 . . DOI: 10.1016/j.cam.2005.07.005 http://doi.org/10.1016/j.cam.2005.07.005 . .

G.E. Stewart , , , G.A. Dumont . . Finite Horizon Based Switching Between Stabilizing Controllers . . American Control Conf. , , 2006 . . p.1550 - - 1556 . . . .

G. Zhai , , , D. Liu , , , J. Imae , , , T. Kobayashi . . Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems . . IEEE Trans. Circ. Syst. Ⅱ , , 2006 . . 53 ( ( 2 ): ): 152 - - 156 . . DOI: 10.1109/TCSII.2005.856033 http://doi.org/10.1109/TCSII.2005.856033 . .

W. Zhang , , , S.Q. Shen , , , Z.Z. Han . . Sufficient conditions for Hurwitz stability of matrices . . Latin Am. Appl. Res. , , 2008 . . 38 253 - - 258 . . . .

Y.H. Zhu , , , D.Z. Cheng , , , H.S. Qin . . Constructing common quadratic Lyapunov functions for a class of stable matrices . . Acta Autom. Sin. , , 2007 . . 33 ( ( 2 ): ): 202 - - 204 . . DOI: 10.1360/aas-007-0202 http://doi.org/10.1360/aas-007-0202 . .

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