Stability radius of implicit dynamic equations with constant coefficients on time scales

This paper deals with the stability radii of implicit dynamic equations on time scales when the structured perturbations act on both the coefficient of derivative and the right-hand side. Formulas of the stability radii are derived as a unification and generalization of some previous results. A special case where the real stability radius and the complex stability radius are equal is studied. Examples are derived to illustrate results.

[1]  Birgit Jacob.  A FORMULA FOR THE STABILITY RADIUS OF TIME-VARYING SYSTEMS , 1998 .

[2]  Nguyen Huu Du,et al.  Stability radii of differential algebraic equations with structured perturbations , 2008, Syst. Control. Lett..

[3]  Huu Du Nguyen,et al.  STABILITY RADII FOR IMPLICIT DIFFERENCE EQUATIONS , 2009 .

[4]  J. J. Dacunha.  Stability for time varying linear dynamic systems on time scales , 2005 .

[5]  Fabian R. Wirth,et al.  Stability radii for positive linear time-invariant systems on time scales , 2010, Syst. Control. Lett..

[6]  Volker Mehrmann,et al.  Generalisation of the Perron–Frobenius theory to matrix pencils , 2008 .

[7]  D. Hinrichsen,et al.  Stability radius for structured perturbations and the algebraic Riccati equation , 1986 .

[8]  Nguyen Huu Du,et al.  Stability radii for linear time-varying differential–algebraic equations with respect to dynamic perturbations , 2006 .

[9]  S. Siegmund,et al.  Exponential Stability of Linear Time-Invariant Systems on Time Scales , 2009 .

[10]  Achim Ilchmann,et al.  Robustness of stability of time-varying linear systems , 1989 .

[11]  S. Hilger.  Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus , 1990 .

[12]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

[13]  Stefan Siegmund,et al.  A spectral characterization of exponential stability for linear time-invariant systems on time scales , 2003 .

[14]  T. Gard,et al.  ASYMPTOTIC BEHAVIOR OF NATURAL GROWTH ON TIME SCALES , 2003 .

[15]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

[16]  Martin Bohner,et al.  Pachpatte Inequalities on Time Scales , 2005 .

[17]  D. Hinrichsen,et al.  The complex stability radius of discrete-time systems and symplectic pencils , 1989, Proceedings of the 28th IEEE Conference on Decision and Control,.

[18]  D. Hinrichsen,et al.  Stability radii of linear systems , 1986 .

[19]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .