$A\in \Bbb R^{n\times n}$ and $B \in \Bbb R ^{n\times m}$. Show that $\exists p\in\Bbb R ^m$ s.t. $(A,Bp)$ is controllable iff $(A,B)$ is controllable

score 286 · Answer 11 · 2013-11-25 20:34:14

286

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Show that the system $\Sigma(SAS^{-1},SB,CS^{-1},D)$ is observable/controllable iff $\Sigma(A,B,C,D)$ is observable/controllable

Published on 25 Nov 2013 - 20:34

score 223 · Answer 12 · 2013-11-30 13:48:10

223

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Which constant matrices $A$ have the property that $\dot{x} =Ax+Bu$ is controllable for every non zero $B$?

Published on 30 Nov 2013 - 13:48

score 201 · Answer 13 · 2013-12-01 18:58:40

201

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Prove $0$ is an exponentially stable equilibrium of the system $x'=f(x)+g(x)$ if $f(0)=g(0)=0$

Published on 01 Dec 2013 - 18:58

score 736 · Answer 14 · 2013-12-02 19:30:21

736

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Affine Non Autonomous State Space system

Published on 02 Dec 2013 - 19:30

score 49 · Answer 15 · 2026-03-30 15:28:33

49

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Extensions to linear control with output constraints

Published on 30 Mar 2026 - 15:28

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$A\in \Bbb R^{n\times n}$ and $B \in \Bbb R ^{n\times m}$. Show that $\exists p\in\Bbb R ^m$ s.t. $(A,Bp)$ is controllable iff $(A,B)$ is controllable

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