A model transformation class for delay-dependent stability analysis

Focuses on some asymptotic stability problems of a class of linear difference-differential equations involving a single delay. Sufficient conditions (expressed in terms of LMIs) for computing the maximal allowable delay are proposed. The novelty of the approach lies on the use of some parametrized model transformations of the initial system. The "optimal" parameters are derived by using a state-feedback construction. The obtained results recover or improve previous delay-independent or delay-dependent criteria from control literature.

[1]  Juing-Huei Su.  Further results on the robust stability of linear systems with a single time delay , 1994 .

[2]  Bor-Sen Chen,et al.  Robust stability of uncertain time-delay systems , 1987 .

[3]  Xi Li,et al.  Criteria for robust stability and stabilization of uncertain linear systems with state delay , 1997, Autom..

[4]  C. Nett,et al.  A new method for computing delay margins for stability of linear delay systems , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[5]  L. Dugard,et al.  Delay-dependent stability of linear systems with delayed state: an LMI approach , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[6]  Jean-Pierre Richard,et al.  Stability of some systems with distributed delay , 1997 .

[7]  M. Ikeda,et al.  Stabilization of Linear Systems with Delay , 1977 .

[8]  Jie Chen,et al.  Asymptotic stability independent of delays: simple necessary and sufficient conditions , 1994, Proceedings of 1994 American Control Conference - ACC '94.

[9]  T. Su,et al.  Robust stability of delay dependence for linear uncertain systems , 1992 .

[10]  Erik I. Verriest,et al.  Stability of Systems with Distributed Delays , 1995 .

[11]  J. Hale,et al.  Stability in Linear Delay Equations. , 1985 .

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

[13]  Jie Chen.  On computing the maximal delay intervals for stability of linear delay systems , 1995, IEEE Trans. Autom. Control..

[14]  T. Mori,et al.  Simple stability criteria for single and composite linear systems with time delays , 1981 .

[15]  M. Fu,et al.  Robust stability and stabilization of time-delay systems via integral quadratic constraint approach , 1998 .

[16]  Vladimir L. Kharitonov,et al.  Robust stability analysis of time delay systems: A survey , 1999 .

[17]  Jean-Michel Dion,et al.  Stability and robust stability of time-delay systems: A guided tour , 1998 .

[18]  J. Richard,et al.  Stability of perturbed systems with time-varying delays , 1997 .

[19]  A. Ivanov,et al.  Robust stability of systems with delayed feedback , 1994 .