Artículos de revistas
Lmi Conditions To Establish The Robustness Of Polytopes Of Polynomial Matrices [condições Lmi Para Estabilidade Robusta De Politopos De Matrizes Polinomiais]
Registro en:
Controle Y Automacao. , v. 15, n. 4, p. 388 - 400, 2004.
1031759
2-s2.0-22044432002
Autor
De Oliveira P.J.
Leite V.J.S.
Oliveira R.C.L.F.
Peres P.L.D.
Institución
Resumen
Sufficient conditions for checking the robust stability of a polytope of polynomial matrices are proposed in this paper. Simple feasibility tests performed in a convex set of linear matrix inequalities defined at the vertices of the polytope yield sufficient conditions for the robust stability of the entire domain. Both continuous-time (left half-plane) and discrete-time stability (unit disk) are investigated. Improved sufficient conditions aie also presented, containing the previous ones as special cases, providing an efficient numerical method for the robust stability analysis of polytopes of polynomial matrices. Numerical comparisons with quadratic stability and with results obtained from other recent methods in the literature show that the proposed conditions provide less conservative evaluations. 15 4 388 400 Ackermann, J., (1993) Robust Control: Systems with Uncertain Parameters, , Springer Verlag, London, England Barmish, B.R., (1994) New Tools for Robustness of Linear Systems, , Macmillan Publishing Company, New York, NY, USA Bartlett, A.C., Hollot, C.V., Lin, H., Root locations of an entire polytope of polynomials: It suffices to check the edges (1988) Mathematics of Control, Signals and Systems, 1, pp. 61-71 Bhattacharyya, S.P., Chapellat, H., Keel, L.H., (1995) Robust Control: The Parametric Approach, , Prentice-Hall Publishing Co., Upper Saddle River, NJ, USA Blondel, V.D., Tsitsiklis, J.N., A survey of computational complexity results in systems and control (2000) Automatica, 36 (9), pp. 1249-1274 Boyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM Studies in Applied Mathematics, Philadelphia, PA Chilali, M., Gabinet, P., ℋ∞, design with pole placement constraints: An LMI approach (1996) IEEE Transactions on Automatic Control, 41 (3), pp. 358-367 De Oliveira, M.C., Bemussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems & Control Letters, 37 (4), pp. 261-265 De Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems (2001) Lecture Notes in Control and Information Science, 268, pp. 241-257. , S. O. Reza Moheimani (ed.), Perspectives in Robust Control, Springer-Verlag, New York Gabinet, P., Nemirovski, A., Laub, A.J., Chilali, M., (1995) LMI Control Toolbox User's Guide, , The Math Works Inc., Natick, MA Geromel, J.C., De Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra and Its Applications, 285 (1-3), pp. 69-80 Geromel, J.C., Peres, P.L.D., Bernussou, J., On a convex parameter space method for linear control design of uncertain systems (1991) SIAM Journal on Control and Optimization, 29 (2), pp. 381-402 Gohberg, I., Lancaster, P., Rodman, L., (1982) Matrix Polynomials, , Academic Press, New York, NY, USA Haddad, W.M., Bernstein, D.S., Controller design with regional pole constraints (1992) IEEE Transactions on Automatic Control, 37 (1), pp. 54-69 Henrion, D., Arzelier, D., Peaucelle, D., Šebek, M., An LMI condition for robust stability of polynomial matrix polytopes (2001) Automatica, 37 (3), pp. 461-468 Henrion, D., Bachelier, O., Šebek, M., D-stability of polynomial matrices (2001) International Journal of Control, 74 (8), pp. 845-846 Kailath, T., (1980) Linear System, , Prentice-Hall, Englewood Cliffs, NJ, USA Karl, W.C., Verghese, G.C., A sufficient condition for the stability of interval matrix polynomials (1993) IEEE Transactions on Automatic Control, 38 (7), pp. 1139-1143 Kharitonov, V.L., Asymptotic stability of an equilibrium position of a family of systems of linear differential equations (1978) Differentsial'nye Uravneniya, 14, pp. 2086-2088 Kučera, V., (1979) Discrete Linear Control: The Polynomial Equation Approach, , Wiley, Chichester, England Leite, V.J.S., Montagner, V.F., De Oliveira, P.J., Oliveira, R.C.L.F., Ramos, D.C.W., Peres, P.L.D., Estabilidade robusta de sistemas lineares através de desigualdades matriciais lineares (2004) Revista Controle & Automação Da SBA, 15 (1), pp. 24-40 Leite, V.J.S., Peres, P.L.D., An improved LMI condition for robust 27-stability of uncertain polytopic systems (2003) IEEE Transactions on Automatic Control, 48 (3), pp. 500-504 Peaucelle, D., Arzelier, D., Bachelier, O., Bemussou, J., A new robust D-stability condition for real convex polytopic uncertainty (2000) Systems & Control Letters, 40 (1), pp. 21-30 Ramos, D.C.W., Peres, P.L.D., A less conservative LMI condition for the robust stability of discrete-time uncertain systems (2001) Systems & Control Letters, 43 (5), pp. 371-378 Ramos, D.C.W., Peres, P.L.D., An LMI approach to compute robust stability domains for uncertain linear systems (2001) Proceedings of the 2001 American Control Conference, 1, pp. 4073-4078. , Arlington, VA Ramos, D.C.W., Peres, P.L.D., An LMI condition for the robust stability of uncertain continuous-time linear systems (2002) IEEE Transactions on Automatic Control, 47 (4), pp. 675-678 Willems, J.C., Paradigms and puzzles in the theory of dynamical systems (1991) IEEE Transactions on Automatic Control, 36 (3), pp. 259-294