Stability and the matrix Lyapunov equation for delay differential systems

Abstract Asymptotic stability independent of the delay of linear differential delay systems with commensurate and non-commensurate delays is analysed using 2-D (two-dimensional) and n-D (n-dimensional) state-space models. Sufficient conditions for stability are obtained in terms of the frequency dependent 1-D (one-dimensional) Lyapunov equations. 2-D and n-D Lyapunov equations with constant parameters are derived using the discrete positive real lemma and the continuous bounded real lemma.

[1]  L. Mirsky,et al.  The Theory of Matrices , 1961, The Mathematical Gazette.

[2]  Louis Weinberg,et al.  Network Analysis and Synthesis , 1962 .

[3]  J. Hale,et al.  Stability of functional differential equations of neutral type , 1970 .

[4]  Brian D. O. Anderson,et al.  Recursive algorithm for spectral factorization , 1974 .

[5]  J. Hale.  Theory of Functional Differential Equations , 1977 .

[6]  R. D. Driver,et al.  Ordinary and Delay Differential Equations , 1977 .

[7]  R. Eising,et al.  Realization and stabilization of 2-d systems , 1978 .

[8]  E. Kamen.  On the relationship between zero criteria for two-variable polynomials and asymptotic stability of delay differential equations , 1980 .

[9]  E. I. Jury,et al.  Stability conditions for a class of delay differential systems , 1982 .

[10]  S. Żak,et al.  On stability independent of delay for linear systems , 1982 .

[11]  N. Bose.  Applied multidimensional systems theory , 1982 .

[12]  Stability analysis and stability conditions in the delay intervals for second-order delay systems , 1984 .

[13]  F. R. Gantmakher.  The Theory of Matrices , 1984 .

[14]  W.-s. Lu,et al.  Comments on "Stability for Two-Dimensional Systems via a Lyapunov Approach , 1985 .

[15]  P. Vaidyanathan.  The discrete-time bounded-real lemma in digital filtering , 1985 .

[16]  E. Lee,et al.  A Lyapunov theory for linear time-delay systems , 1986 .

[17]  Brian D. O. Anderson,et al.  Stability and the matrix Lyapunov equation for discrete 2-dimensional systems , 1986 .

[18]  A. Hmamed,et al.  Stability conditions of delay-differential systems , 1986 .

[19]  Stanislaw H. Zak,et al.  On the stabilization of linear neutral delay-differential systems , 1986 .

[20]  Stanislaw H. Zak,et al.  Realizations of 2-D filters and time delay systems , 1986 .

[21]  Panajotis Agathoklis,et al.  The Lyapunov equation for n-dimensional discrete systems , 1988 .

[22]  Panajotis Agathoklis.  Conditions for the 2-D characteristic polynomial of a matrix to be very strict Hurwitz , 1989, IEEE Trans. Acoust. Speech Signal Process..