Proof of marginal stability
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Given a homogeneous continuous linear time invariant system:
$$ fracdx(t)dt = Ax(t) ;,; A in mathbbR^ntimes n,; x(t) in mathbbR^n,; t ge 0 $$
Is there any reference (book or web page) to the proof that this system is marginally stable if and only if the real part of every eigenvalue (of the Jordan matrix associated to A) is non-positive such that one or more eigenvalues have zero real part, and all eigenvalues with zero real part are simple roots?
linear-algebra control-theory
add a comment |Â
up vote
1
down vote
favorite
Given a homogeneous continuous linear time invariant system:
$$ fracdx(t)dt = Ax(t) ;,; A in mathbbR^ntimes n,; x(t) in mathbbR^n,; t ge 0 $$
Is there any reference (book or web page) to the proof that this system is marginally stable if and only if the real part of every eigenvalue (of the Jordan matrix associated to A) is non-positive such that one or more eigenvalues have zero real part, and all eigenvalues with zero real part are simple roots?
linear-algebra control-theory
Are you more interested in the proof, or in having a reference?
â Kwin van der Veen
Sep 9 at 9:46
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
Given a homogeneous continuous linear time invariant system:
$$ fracdx(t)dt = Ax(t) ;,; A in mathbbR^ntimes n,; x(t) in mathbbR^n,; t ge 0 $$
Is there any reference (book or web page) to the proof that this system is marginally stable if and only if the real part of every eigenvalue (of the Jordan matrix associated to A) is non-positive such that one or more eigenvalues have zero real part, and all eigenvalues with zero real part are simple roots?
linear-algebra control-theory
Given a homogeneous continuous linear time invariant system:
$$ fracdx(t)dt = Ax(t) ;,; A in mathbbR^ntimes n,; x(t) in mathbbR^n,; t ge 0 $$
Is there any reference (book or web page) to the proof that this system is marginally stable if and only if the real part of every eigenvalue (of the Jordan matrix associated to A) is non-positive such that one or more eigenvalues have zero real part, and all eigenvalues with zero real part are simple roots?
linear-algebra control-theory
linear-algebra control-theory
asked Sep 8 at 13:24
Daniel
555
555
Are you more interested in the proof, or in having a reference?
â Kwin van der Veen
Sep 9 at 9:46
add a comment |Â
Are you more interested in the proof, or in having a reference?
â Kwin van der Veen
Sep 9 at 9:46
Are you more interested in the proof, or in having a reference?
â Kwin van der Veen
Sep 9 at 9:46
Are you more interested in the proof, or in having a reference?
â Kwin van der Veen
Sep 9 at 9:46
add a comment |Â
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Are you more interested in the proof, or in having a reference?
â Kwin van der Veen
Sep 9 at 9:46