TY - JOUR
T1 - A necessary condition for quantitative exponential stability of linear state-space systems
AU - Lewkowicz, Izchak
PY - 1999/9/15
Y1 - 1999/9/15
N2 - For an arbitrary n × n constant matrix A the two following facts are well known: • (1/n)Re(trace A) - maxj=i,...,nRe λj(A4)≤0; • If U is a unitary matrix, one can always find a skew-Hermitian matrix A so that U = eA. In this note we present the extension of these two facts to the context of linear time-varying dynamical systems ẋ = A(t)x, t≥0. As a by-product, this result suggests that, the notion of "slowly varying state-space systems", commonly used in literature, is mathematically not natural to the problem of exponential stability.
AB - For an arbitrary n × n constant matrix A the two following facts are well known: • (1/n)Re(trace A) - maxj=i,...,nRe λj(A4)≤0; • If U is a unitary matrix, one can always find a skew-Hermitian matrix A so that U = eA. In this note we present the extension of these two facts to the context of linear time-varying dynamical systems ẋ = A(t)x, t≥0. As a by-product, this result suggests that, the notion of "slowly varying state-space systems", commonly used in literature, is mathematically not natural to the problem of exponential stability.
KW - Convergence rate
KW - Exponential stability
KW - Necessary condition
KW - Slowly time-varying
UR - http://www.scopus.com/inward/record.url?scp=0347026131&partnerID=8YFLogxK
U2 - 10.1016/S0167-6911(99)00031-6
DO - 10.1016/S0167-6911(99)00031-6
M3 - Article
AN - SCOPUS:0347026131
VL - 38
SP - 1
EP - 4
JO - Systems and Control Letters
JF - Systems and Control Letters
SN - 0167-6911
IS - 1
ER -