Robust stability conditions for polytopic systems

International Journal of Systems Science

Volumn 36, Issue 15, 2005, Pages 961-973

  Grman, Ĺubomír ^a,b   Rosinová, Danica ^a,c   Veselý, Vojtech ^a,b,c   Kozáková, Alena ^a,c  

^a SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^b STU FEI ^*  (Slovakia)

^c IEEE

Author keywords

LMI conditions; Lyapunov function; Robust stability

Indexed keywords

LMI CONDITIONS; LYAPUNOV FUNCTION; POLYTOPIC UNCERTAINTY;

DISCRETE TIME CONTROL SYSTEMS; FUNCTIONS; LYAPUNOV METHODS;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 32144443991     PISSN: 00207721     EISSN: 14645319     Source Type: Journal    
DOI: 10.1080/00207720500389592     Document Type: Article

References (17)

1. A.C. Bartlett, C.V. Hollot and H. Lin, "Root location of an entire polytope of polynomials: it suffices to check the edges", Mathematics of Control, Signals and Systems, 1, pp. 61-71, 1988.
2. R.E. Benton and D. Smith, "A non-iterative LMI based algorithm for robust static output feedback stabilization", Int. Journal of Control, 72, pp. 1322-1330, 1999.
3. S.P. Bhattacharyya, H. Chapellat and L.H. Keel, Robust Control: The Parametric Approach, N.J.: Prentice Hall, Englewood Cliffs, 1995.
4. S. Boyd, L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia: SIAM Studies in Applied Mathematics, 1994.
5. ∞ control problems", IEEE Trans. Circuits and Systems, 34, pp. 831-847, 1989.
6. Y. Ebihara and T. Hagiwara, "New dilated LMI characterizations for continuous-time control design and robust multiobjectivc control", in American Control Conference, 2002, Anchorage, USA, pp. 47-52.
7. M.K.H. Fan, A.L. Tits and J.C. Doyle, "Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics", IEEE Trans. Circuits and Systems, 36, pp. 25-38, 1991.
8. P. Gahinet, P. Apkarian and M. Chilali, "Affine parameter-dependent Lyapunov functions and real parametric uncertainty", IEEE Trans. Circuits and Systems, 41, pp. 436-442, 1996.
9. D. Henrion, D. Arzelier and D. Peaucelle, "Positive polynomial matrices and improved LMI Robustness Conditions", in 15th IFAC World Congress, 2002, Barcelona, Spain, CD-ROM.
10. V.L. Kharitonov, "Asymptotic stability of an equilibrium position of a family of systems of linear differential equations", Differential Equations, 14, pp. 1483-1485, 1979.
11. M.C. de Oliveira, J. Bernussou and J.G. Geromel, "A new discrete-time robust stability condition", Systems and Control Letters, 37, pp. 261-265, 1999.
12. D. Peaucelle, D. Arzelier, O. Bachelier and J. Bernussou, "A new robust D-stability condition for real convex polytopic uncertainty", Systems and Control Letters, 40, pp. 21-30, 2000.
13. D. Rosinová and V. Veselý, "Robust output feedback design of linear discrete-time systems - LMI Approach", in 4th IFAC Symposium Robust Control Design, 2003, Bratislava, Slovakia, CD-ROM.
14. R.H.C. Takahashi, D.C.W. Ramos and P.L.D. Peres, "Robust control synthesis via a genetic algorithm and LMI's", in 15th IFAC World Congress, 2002, Barcelona, Spain, CD-ROM.
15. V. Veselý, "Robust output feedback controller design for linear parametric uncertain systems", Journal of Electrical Engineering, 53, pp. 117-125, 2002.
16. V. Veselý, "Robust output feedback control synthesis: LMI approach", in 2nd IFAC Conference 'Control Systems Design', 2003, Bratislava, Slovakia, CD-ROM.
17. G. Zames, "Feedback and optimal sensitivity: model reference transformations, multiplicative semi norms and approximate inverses", IEEE Trans. Circuits and Systems, 26, pp. 301-320, 1981.