LMI based robust stability conditions for linear uncertain systems: a numerical comparison

In the 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 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.

[1]  P. Peres,et al.  a linear programming oriented procedure for quadratic stabilization of uncertain systems , 1989 .

[2]  J. Geromel,et al.  A new discrete-time robust stability condition , 1999 .

[3]  B. Barmish.  Necessary and sufficient conditions for quadratic stabilizability of an uncertain system , 1985 .

[4]  E. Feron,et al.  Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions , 1996, IEEE Trans. Autom. Control..

[5]  Pedro L. D. Peres,et al.  An LMI approach to compute robust stability domains for uncertain linear systems , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[6]  Anders Rantzer,et al.  Piecewise linear quadratic optimal control , 1997, Proceedings of the 1997 American Control Conference (Cat. No.97CH36041).

[7]  Liu Hsu,et al.  LMI characterization of structural and robust stability , 1998 .

[8]  J. Bernussou,et al.  A new robust D-stability condition for real convex polytopic uncertainty , 2000 .

[9]  Robert E. Skelton,et al.  Stability tests for constrained linear systems , 2001 .

[10]  Pedro Luis Dias Peres,et al.  An LMI condition for the robust stability of uncertain continuous-time linear systems , 2002, IEEE Trans. Autom. Control..

[11]  S. Bittanti,et al.  Affine Parameter-Dependent Lyapunov Functions and Real Parametric Uncertainty , 1996 .

[12]  Pedro Luis Dias Peres,et al.  A less conservative LMI condition for the robust stability of discrete-time uncertain systems , 2001, Syst. Control. Lett..