Diagonal stability of uncertain interval systems

In this paper we consider the problem of diagonal stability of interval systems. We investigate the existence and evaluation of a common diagonal solution to the Lyapunov and Stein matrix inequalities for third order interval systems. We show that these problems are equivalent to minimax problem with polynomial goal functions. We suggest an interesting approach to solve the corresponding game problems. This approach uses the opennes property of the set of solutions. Examples show that the proposed method is effective and sufficiently fast.

[1]  H. Khalil.  On the existence of positive diagonal P such that PA + A^{T}P l 0 , 1982 .

[2]  E. Kaszkurewicz,et al.  Matrix diagonal stability in systems and computation , 1999 .

[3]  K. Narendra,et al.  On the existence of diagonal solutions to the Lyapunov equation for a third order system , 2003, Proceedings of the 2003 American Control Conference, 2003..

[4]  B. Ross Barmish,et al.  New Tools for Robustness of Linear Systems , 1993 .

[5]  Eduardo D. Sontag,et al.  Diagonal stability of a class of cyclic systems and its connection with the secant criterion , 2006, Autom..

[6]  Daniel Liberzon,et al.  Common Lyapunov functions and gradient algorithms , 2004, IEEE Transactions on Automatic Control.

[7]  Vakif Dzhafarov,et al.  Common diagonal stability of second order interval systems , 2014, 2014 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO).

[8]  J. Rohn.  Positive Definiteness and Stability of Interval Matrices , 1994, SIAM J. Matrix Anal. Appl..

[9]  Mariusz Ziolko.  Application of Lyapunov functionals to studying stability of linear hyperbolic systems , 1990 .

[10]  Taner Büyükköroglu.  Common diagonal Lyapunov function for third order linear switched system , 2012, J. Comput. Appl. Math..

[11]  Shankar P. Bhattacharyya,et al.  Robust Control: The Parametric Approach , 1995 .

[12]  O. Pastravanu,et al.  Sufficient conditions for Schur and Hurwitz diagonal stability of complex interval matrices , 2015 .