On LMI robust D-stability condition for real convex polytopic uncertainty

In this paper, a new sufficient LMI condition for the robust stability is established with respect to polytopic uncertainty. The robust stability of the uncertain systems can be verified by means of the feasibility of a set of LMIs described only in terms of the vertices of the polytopic domain. This approach is less conservative than quadratic stability by using a parameter-dependent Lyapunov function and extends the results of the related references.

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

[2]  J. Geromel,et al.  LMI characterization of structural and robust stability: the discrete-time case , 1999 .

[3]  Vladimir A. Yakubovich,et al.  Linear Matrix Inequalities in System and Control Theory (S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan) , 1995, SIAM Rev..

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

[5]  Liu Hsu,et al.  LMI characterization of structural and robust stability , 1998, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).

[6]  Youxian Sun,et al.  On robust admissibility condition for descriptor systems with convex polytopic uncertainty , 2003, Proceedings of the 2003 American Control Conference, 2003..

[7]  E. Yaz.  Linear Matrix Inequalities In System And Control Theory , 1998, Proceedings of the IEEE.

[8]  M. C. D. Oliveiraa,et al.  A new discrete-time robust stability condition ( , 1999 .

[9]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[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]  P. Gahinet,et al.  H∞ design with pole placement constraints: an LMI approach , 1996, IEEE Trans. Autom. Control..

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

[13]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.