On the stability of slowly time-varying linear systems

New conditions are given in both deterministic and stochastic settings for the stability of the system x=A(t)x when A(t) is slowly varying. Roughly speaking, the eigenvalues of A(t) are allowed to “wander” into the right half-plane as long as “on average” they are strictly in the left half-plane.

[1]  Han-Fu Chen,et al.  Identification and Stochastic Adaptive Control , 1991 .

[2]  J. A. Richards.  Analysis of periodically time-varying systems , 1983 .

[3]  L. Y. Wang,et al.  Local-global double algebras for slow H/sup infinity / adaptation. I. Inversion and stability , 1991 .

[4]  Charles A. Desoer,et al.  Slowly varying system ẋ = A(t)x , 1969 .

[5]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .

[6]  Le Yi Wang,et al.  Local–global double algebras for slow H∞ adaptation; the case of l2 disturbances , 1989 .

[7]  S. Sastry,et al.  Adaptive Control: Stability, Convergence and Robustness , 1989 .

[8]  D. Mayne,et al.  Design issues in adaptive control , 1988 .

[9]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[10]  G. Goodwin,et al.  Adaptive control of time-varying linear systems , 1988 .

[11]  B. L. Ly,et al.  Almost-Sure Stability of Some Linear Stochastic Systems , 1989 .

[12]  Anuradha M. Annaswamy,et al.  Stable Adaptive Systems , 1989 .

[13]  Petros A. Ioannou,et al.  Adaptive control of linear time-varying plants: a new model reference controller structure , 1989 .

[14]  P. Billingsley,et al.  Probability and Measure , 1980 .

[15]  Petros A. Ioannou,et al.  Adaptive control of linear time-varying plants , 1987, Autom..

[16]  R. Khasminskii.  Stochastic Stability of Differential Equations , 1980 .

[17]  G. Kreisselmeier.  Adaptive control of a class of slowly time-varying plants , 1986 .

[18]  G. Blankenship,et al.  Stability of linear differential equations with random coefficients , 1977 .

[19]  E. F. Infante,et al.  On the Stability of Some Linear Nonautonomous Random Systems , 1968 .

[20]  H. H. Rosenbrook.  The Stability of Linear Time-dependent Control Systems† , 1963 .

[21]  T. Apostol.  Mathematical Analysis , 1957 .

[22]  W. A. Coppel.  Dichotomies in Stability Theory , 1978 .

[23]  N. Wiener.  The Fourier Integral: and certain of its Applications , 1933, Nature.

[24]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .