Robust stability and diagonal Liapunov functions

It is shown that diagonal Liapunov functions play an essential role in the robust stability problem of linear autonomous continuous and discrete-time systems in state-space form, subjected to a broad class of perturbations. The results obtained generalize a well-known result of Persidskii (1969) and are related to a variety of similar results in the literature. Techniques are suggested for the application of the results to the problem of evaluating robust stability bounds in different contexts. Several examples are given.<<ETX>>

[1]  M. Fiedler,et al.  On matrices with non-positive off-diagonal elements and positive principal minors , 1962 .

[2]  James Quirk,et al.  Qualitative Problems in Matrix Theory , 1969 .

[3]  M. Araki,et al.  Stability and transient behavior of composite nonlinear systems , 1972 .

[4]  B. Goh,et al.  Nonvulnerability of ecosystems in unpredictable environments. , 1976, Theoretical population biology.

[5]  G. S. Ladde,et al.  Cellular systems—II. stability of compartmental systems , 1976 .

[6]  R. V. Patel,et al.  Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [application to Augmentor Wing Jet STOL Research Aircraft flare control autopilot design] , 1977 .

[7]  V. Klee,et al.  When is a Matrix Sign Stable? , 1977, Canadian Journal of Mathematics.

[8]  R. V. Patel,et al.  Robustness of linear quadratic state feedback designs in the presence of system uncertainty. [applied to STOL autopilot design , 1977 .

[9]  B. Goh.  Global Stability in Many-Species Systems , 1977, The American Naturalist.

[10]  P. Moylan,et al.  Matrices with positive principal minors , 1977 .

[11]  A. Berman,et al.  Positive diagonal solutions to the Lyapunov equations , 1978 .

[12]  R. Roberts,et al.  Digital filter realizations without overflow oscillations , 1978 .

[13]  Liu Hsu,et al.  Structural Properties in the Stability Problem of Interconnected Systems , 1980 .

[14]  Charles R. Johnson,et al.  A Semi-Definite Lyapunov Theorem and the Characterization of Tridiagonal D-Stable Matrices , 1982 .

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

[16]  Abraham Berman,et al.  Matrix Diagonal Stability and Its Implications , 1983 .

[17]  E. Kaszkurewicz,et al.  A result on stability of nonlinear discrete time systems and its application to recursive digital filters , 1984, The 23rd IEEE Conference on Decision and Control.

[18]  Liu Hsu,et al.  On two classes of matrices with positive diagonal solutions to the Lyapunov equation , 1984 .

[19]  A note on the absolute stability of non-linear discrete-time systems , 1984 .

[20]  A. Michel,et al.  Stability analysis of discrete- time interconnected systems via computer-generated Lyapunov functions with applications to digital filters , 1985 .

[21]  Jose C. Geromel,et al.  On the determination of a diagonal solution of the Lyapunov equation , 1985 .

[22]  J C Geromel,et al.  On The Robustness Of Linear Continuous-time Dynamic Systems. , 1986 .

[23]  Shankar P. Bhattacharyya,et al.  Robust Stabilization Against Structured Perturbations , 1987 .

[24]  J. C. Geromel,et al.  On the robustness of optimal regulators for nonlinear discrete-time systems , 1987 .

[25]  Hui Hu,et al.  An algorithm for rescaling a matrix positive definite , 1987 .

[26]  Comment on ‘Stability of interval matrices’ , 1987 .

[27]  Dragoslav D. Šiljak,et al.  Robust stability of discrete systems , 1988 .

[28]  D. Siljak.  Parameter Space Methods for Robust Control Design: A Guided Tour , 1988, 1988 American Control Conference.

[29]  D. Siljak,et al.  On the convergence of parallel asynchronous block-iterative computations , 1990 .