# Tagged Questions

Control theory is an interdisciplinary branch of engineering and mathematics that deals with the behavior of dynamical systems with inputs. The external input of a system is called the reference. When one or more output variables of a system need to follow a certain reference over time, a controller ...

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### Derivation for state equation linearization

In the following notes, how to linearize a state equation is described. The part I don't understand is why you can just remove the $\delta$ like that. I think the state equation should be: \begin{...
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### matrix inequality proof [completion of squares]

Can someone help me to prove this? $\begin{bmatrix} 0 & B^\top W^\top \\ WB & 0 \end{bmatrix} \leq \begin{bmatrix} B^\top Q B & 0 \\0 & W^\top Q^{-1}W \end{bmatrix}$ with $Q$ ...
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### From multivariable system transfer function matrix to state space representation

I have the transfer function matrix $H(s) = \begin{bmatrix} {1\over s+1} & {2\over s+2} \\ {-2\over s^2+3s+2} & {2s\over s+1} \\ \end{bmatrix}$ And I want to ...
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### Given dynamic system $\dot x = Ax + Bu$, how can we prove that $M$ = {$(A,B)$: system is controllable} is an open set on an Euclidean space?

I wish to show that $M$ = {$(A,B)$: system is controllable} is an open set in some Euclidean space. Equivalently, how can we show that the complement to this set is closed? Here Controllability ...
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### Control theory- basic question on stabilizabilty

Studying some control theory but having difficulty learning because my lecturer doesn't provide solutions to any of his exercises AT ALL. Below I've attached a problem I've just done and my answers ...
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### Stability of zero-order hold controllers for linear systems

From what I've read, Lyapunov functions provide a very nice mechanism for verifying stability of continuous-time linear systems (non-linear as well, but that's not my concern at the moment). For ...
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### Control theory with state and input constraints

What are some control theory tools for solving problems of the following form?: Given a system model, control input constraints $I$, and control output constraints $O$, what is the largest set ...