Matrix Quadratic Polynomials With Application To Robust Stability Analysis

This paper provides robust stability conditions for continuous and discrete time polytopic systems. They are obtained from linear and fractional parameter dependent Lyapunov functions and are expressed in terms of linear matrix inequalities-LMI. As an immediate generalization, a tight upper bound of the associated guaranteed H2 cost is determined. Numerical examples are included for illustration and comparison purpose with other robust stability conditions for continuous and discrete time systems available in the literature to date. Copyright © 2005 IFAC.5PART 1549554Apkarian, P., Tuan, H.D., Parameterized LMIs in control theory (2000) SIAM on Control Optim., 38 (4), pp. 1241-1264Bliman, P.A., A convex approach to robust stability for linear systems with uncertain scalar parameters (2004) SIAM on Control Optim., 42 (46), pp. 2016-2042Boyd, S.P., El Ghaoui, L., Feron, E., Balakrishnan, V., (1994) Linear Matrix Inequalities in System and Control Theory, , SIAM, Philadelphia, 1994Chesi, G., Garulli, A., Tesi, A., Vicino, A., Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems : An LMI approach (2005) IEEE Trans. Automat. Contr., 50 (3), pp. 365-379Dettori, M., Scherer, C.W., New robust stability and performance conditions based on parameter dependent multipliers (2000) Proccedings of IEEE CDC, , Sydney, AustraliaGahinet, P., Apkarian, P., Chilali, M., Affine parameter-dependent Lyapunov functions and real parametric uncertainty (1996) IEEE Transactions on Automatic Control, 41 (3), pp. 436-442. , PII S0018928696021216Geromel, 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 Optim., 29 (2), pp. 381-402Geromel, J.C., De Oliveira, M.C., Hsu, L., LMI characterization of structural and robust stability (1998) Linear Algebra Appl., 285, pp. 69-80Luenberger, D.G., (1979) Introduction to Dynamic Systems : Theory, Models and Applications, 1979. , John Wiley $ Sons, New YorkDe Oliveira, M.C., Geromel, J.C., Hsu, L., LMI characterization of structural and robust stability: The discrete-time case (1999) Linear Algebra and Its Applications, 296 (1-3), pp. 27-38. , PII S0024379599000865De Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems and Control Letters, 37 (4), pp. 261-265. , PII S0167691199000353Ramos, D.C.W., Peres, P.L.D., A less conservative LMI condition for the robust stability of discrete-time uncertain systems (2001) Systems and Control Letters, 43 (5), pp. 371-378. , DOI 10.1016/S0167-6911(01)00120-7, PII S0167691101001207Ramos, 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. , DOI 10.1109/9.995048, PII S0018928602037509Trofino, A., De Souza, C.E., Biquadratic stability of uncertain linear systems (2001) IEEE Transactions on Automatic Control, 46 (8), pp. 1303-1307. , DOI 10.1109/9.940939, PII S001892860107693