Lmi Based Robust Stability Conditions For Linear Uncertain Systems: A Numerical Comparison

In this paper, several numerical experiments are performed in order to compare three linear matrix inequalities based sufficient conditions for the robust stability of linear systems in polytopic domains. The conditions are the quadratic stability and two recently appeared robust stability conditions based on parameter dependent Lyapunov functions: one using extra variables and augmented equations and the other using a larger number of equations. From the examples, it is possible to infer about the conservativeness of the conditions and also about the cases in which an equivalence exists. Both continuous-time and discrete-time systems are investigated.1644649Barmish, B.R., Necessary and sufficient conditions for quadratic stabilizability of an uncertain system (1985) Journal of Optimization Theory and Applications, 46 (4), pp. 399-408. , AugustBernussou, J., Peres, P.L.D., Geromel, J.C., A linear programming oriented procedure for quadratic stabilization of uncertain systems (1989) Systems & Control Letters, 13 (1), pp. 65-72. , JulyBoyd, S., El Ghaoui, L., Feron, E., Balakrishnan, V., Linear matrix inequalities in system and control theory (1994) SIAM Studies in Applied Mathematics, , Philadelphia, USADe Oliveira, M.C., Bernussou, J., Geromel, J.C., A new discrete-time robust stability condition (1999) Systems & Control Letters, 37 (4), pp. 261-265. , JulyDe Oliveira, M.C., Skelton, R.E., Stability tests for constrained linear systems (2001) Perspectives in Robust Control, Lecture Notes in Control and Information Science, pp. 241-257. , In S. O. Reza Moheimani, editorSpringer-VerlagFeron, E., Apkarian, P., Gahinet, P., Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions (1996) IEEE Transactions on Automatic Control, 41 (7), pp. 1041-1046. , JulyGahinet, 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. , MarchGahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., (1995) LMI Control Toolbox for Use with Matlab. User's Guide, , The Math Works IncGeromel, 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. , DecemberPeaucelle, D., Arzelier, D., Bachelier, O., Bernussou, J., A new robust D-stability condition for real convex polytopic uncertainty (2000) Systems & Control Letters, 40 (1), pp. 21-30. , MayRamos, 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. , AugustRamos, D.C.W., Peres, P.L.D., An LMI approach to compute robust stability domains for uncertain linear systems (2002) IEEE Transactions on Automatic Control, 47 (4), pp. 675-678. , AprilRantzer, A., Johansson, M., Piecewise linear quadratic optimal control (2000) IEEE Transactions on Automatic Control, 45 (4), pp. 629-637. , Apri