Full Text:   <2561>

CLC number: TP273

On-line Access: 2012-10-01

Received: 2012-03-19

Revision Accepted: 2012-07-31

Crosschecked: 2012-09-11

Cited: 0

Clicked: 4581

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.10 P.781-792


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

Author(s):  Mohd Amin At-Tasneem, Sallehuddin Mohamed Haris, Zulkifli Mohd Nopiah

Affiliation(s):  Faculty of Mechanical Engineering, University Malaysia Pahang, Pekan 26600, Malaysia; more

Corresponding email(s):   tasneem@ump.edu.my, salleh@eng.ukm.my, zmn@eng.ukm.my

Key Words:  Linear inequalities, Hybrid systems, Stability, Common quadratic Lyapunov function, Numerical computation, Symbolic computation

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]. Journal of Zhejiang University Science C, 2012, 13(10): 781-792.

@article{title="A computing capability test for a switched system control design using the Haris-Rogers method",
author="Mohd Amin At-Tasneem, Sallehuddin Mohamed Haris, Zulkifli Mohd Nopiah",
journal="Journal of Zhejiang University Science C",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T A computing capability test for a switched system control design using the Haris-Rogers method
%A Mohd Amin At-Tasneem
%A Sallehuddin Mohamed Haris
%A Zulkifli Mohd Nopiah
%J Journal of Zhejiang University SCIENCE C
%V 13
%N 10
%P 781-792
%@ 1869-1951
%D 2012
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C1200074

T1 - A computing capability test for a switched system control design using the Haris-Rogers method
A1 - Mohd Amin At-Tasneem
A1 - Sallehuddin Mohamed Haris
A1 - Zulkifli Mohd Nopiah
J0 - Journal of Zhejiang University Science C
VL - 13
IS - 10
SP - 781
EP - 792
%@ 1869-1951
Y1 - 2012
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C1200074

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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

[2]Decarlo, R.A., Branicky, M.S., Pettersson, S., Lennartson, B., 2000. Perspectives and results on the stability and stabilizability of hybrid systems. Proc. IEEE, 88(7):1069-1082.

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

[4]Grant, M., Boyd, S., 2012. Cvx Users’ Guide for Cvx Version 1.21.

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

[6]Haris, S.M., Rogers, E., 2008. A Matlab Toolbox for Finding Stabilizing Controllers for a Class of Switched Systems. Int. Conf. on Computational Intelligence for Modelling Control & Automation, p.238-242.

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

[8]Hespanha, J.P., Morse, A.S., 2002. Switching between stabilizing controllers. Automatica, 38(11):1905-1917.

[9]King, C., Shorten, R., 2006. 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., 413(1):24-35.

[10]Liberzon, D., Hespanha, J.P., Morse, A.S., 1999. Stability of switched systems: a Lie-algebraic condition. Syst. Control Lett., 37(3):117-122.

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

[12]Montagner, V.F., Leite, V.J.S., Oliveira, R.C.L.F., Peres, P.L.D., 2006. State feedback control of switched linear systems: an LMI approach. J. Comput. Appl. Math., 194(2):192-206.

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

[14]Zhai, G., Liu, D., Imae, J., Kobayashi, T., 2006. Lie algebraic stability analysis for switched systems with continuous-time and discrete-time subsystems. IEEE Trans. Circ. Syst. II, 53(2):152-156.

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

[16]Zhu, Y.H., Cheng, D.Z., Qin, H.S., 2007. Constructing common quadratic Lyapunov functions for a class of stable matrices. Acta Autom. Sin., 33(2):202-204.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2022 Journal of Zhejiang University-SCIENCE