Stability of Discrete Linear Systems with Periodic Coefficients under Parametric Perturbations
This paper studies the problem of exponential
stability of perturbed discrete linear systems with periodic
coefficients. Assuming that the unperturbed system is exponentially
stable we obtain conditions on the perturbations under which the
perturbed system is exponentially stable.
[1] K. Aydin, H. Bulgak and G.V. Demidenko, Numeric characteristics
for asymptotic stability of solutions to linear difference equations with
periodic coefficients, Siberian Mathematical Journal, vol. 41, pp.
1227-1237, 2000.
[2] K. Aydin, H. Bulgak and G.V. Demidenko, Asymptotic stability of
solutions to perturbed difference equations with periodic coefficients,
Siberian Mathematical Journal, vol. 43, pp. 389-401, 2002.
[3] R. P. Agarwal, Difference Equations and Inequalities. Theory,
Methods, and Applications (Marcel Dekker, New York, 2000).
[4] S. Bittanti and P. Colaneri, Invariant representation of discrete-time
periodic systems, Automatica vol. 36, pp. 1777-1793, 2000.
[5] S. Barnett, R. G Cameron, Introduction to Mathematical Control
Theory (2nd Edition, Clarendon Press, Oxford, 1985).
[6] D. Hinrichsen and A. J. Pritchard, Stability radii of Linear Systems,
Systems and Control Letters, vol. 7, pp. 1-10, 1986.
[7] D. Hinrichsen and A. J. Pritchard, Mathematical systems theory I
(vol. 48 of texts in Applied Mathematics, Springer-Verlag, Berlin
2005).
[8] H. O. Kreiss, Űber die stabilitätsdefinition fur
Differenzengleichungen, die partielle Differentialgleichungen
approximieren, BIT 2, vol. 2, pp. 153-181, 1962.
[9] M. Robbé and M. Sadkane, Discrete-time Lyapunov stability of large
matrices, Journal of Computational and Applied Mathematics, vol.
115, pp. 479-494, 2000.
[10] M. Sadkane, L. Grammont, A note on the Lyapunov stability of
periodic discrete-time systems, Journal of Computational and Applied
Mathematics, vol. 176, pp. 463-466, 2005.
[11] A. Varga, An overview of recent developments in computational
methods for periodic systems, Proceedings of IFAC Workshop on
Periodic Control Systems, St. Petersburg, Russia, 2007.
[12] F. Wirth, On the calculation of time-varying stability radii,
International Journal on Robust Nonlinear Control, vol. 8, pp. 1043-
1058, 1998.
[1] K. Aydin, H. Bulgak and G.V. Demidenko, Numeric characteristics
for asymptotic stability of solutions to linear difference equations with
periodic coefficients, Siberian Mathematical Journal, vol. 41, pp.
1227-1237, 2000.
[2] K. Aydin, H. Bulgak and G.V. Demidenko, Asymptotic stability of
solutions to perturbed difference equations with periodic coefficients,
Siberian Mathematical Journal, vol. 43, pp. 389-401, 2002.
[3] R. P. Agarwal, Difference Equations and Inequalities. Theory,
Methods, and Applications (Marcel Dekker, New York, 2000).
[4] S. Bittanti and P. Colaneri, Invariant representation of discrete-time
periodic systems, Automatica vol. 36, pp. 1777-1793, 2000.
[5] S. Barnett, R. G Cameron, Introduction to Mathematical Control
Theory (2nd Edition, Clarendon Press, Oxford, 1985).
[6] D. Hinrichsen and A. J. Pritchard, Stability radii of Linear Systems,
Systems and Control Letters, vol. 7, pp. 1-10, 1986.
[7] D. Hinrichsen and A. J. Pritchard, Mathematical systems theory I
(vol. 48 of texts in Applied Mathematics, Springer-Verlag, Berlin
2005).
[8] H. O. Kreiss, Űber die stabilitätsdefinition fur
Differenzengleichungen, die partielle Differentialgleichungen
approximieren, BIT 2, vol. 2, pp. 153-181, 1962.
[9] M. Robbé and M. Sadkane, Discrete-time Lyapunov stability of large
matrices, Journal of Computational and Applied Mathematics, vol.
115, pp. 479-494, 2000.
[10] M. Sadkane, L. Grammont, A note on the Lyapunov stability of
periodic discrete-time systems, Journal of Computational and Applied
Mathematics, vol. 176, pp. 463-466, 2005.
[11] A. Varga, An overview of recent developments in computational
methods for periodic systems, Proceedings of IFAC Workshop on
Periodic Control Systems, St. Petersburg, Russia, 2007.
[12] F. Wirth, On the calculation of time-varying stability radii,
International Journal on Robust Nonlinear Control, vol. 8, pp. 1043-
1058, 1998.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63590", author = "Adam Czornik and Aleksander Nawrat", title = "Stability of Discrete Linear Systems with Periodic Coefficients under Parametric Perturbations", abstract = "This paper studies the problem of exponential
stability of perturbed discrete linear systems with periodic
coefficients. Assuming that the unperturbed system is exponentially
stable we obtain conditions on the perturbations under which the
perturbed system is exponentially stable.", keywords = "Exponential stability, time-varying linear systems,periodic systems.", volume = "5", number = "3", pages = "490-4", }
