Questions tagged [linear-control]

Linear control theory is the sub-branch of control theory dealing with linear or linearized systems.

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Markov Decision Processes and Control Engineering?

In a Markov Decision Process, one has a Markov chain with (left) regular stochastic matrix $P$ and a collection of "actions" $a_i$ one can have act on the system after it transitions via its ...
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Balancing Transformation of Linear Time Invariant Systems

I've been experimenting with linear time invariant systems. In particular I've been playing around with the concept of balanced truncation. All the resources I've found only explain how to do balanced ...
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Proving a transfer function is proper or not

I'm trying to prove (not just show) whether the following transfer function is proper or not $$G(s) = \frac{1}{1+se^{-s}}$$ A transfer function $G(s)$ is said to be proper if there is $\alpha \geq 0$...
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Model building a container

in this question I'm supposed to make an equation for the height of fluid in the container the container is cylinder form with base area of $A_0 =1261 m^2$. The variables are $V$ inflow stream. $W$ ...
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Show $\lim \limits_{t \to \infty} x(t) = 0$ exponentially for any $x(0)\in \mathbb{R}^n$ if $\lim \limits_{t \to \infty} u(t) = 0$ exponentially.

I'd like to ask a question about the controllability of a linear system. Any help would be appreciated. Given a vector $x(t)\in \mathbb{R}^n$ defined over [$0$, $\infty$), we say $x(t)$ converge ...
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Inverse dynamics control: Proof of asymptotic stability of error system

The inverse dynamics control in robotic applications yields the error system \begin{equation} \ddot{\mathbf{e}} + \mathbf{K}_1 \dot{\mathbf{e}} + \mathbf{K}_0 {\mathbf{e}} = \mathbf{0} \end{equation} ...
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How can I do Model Reference Adaptive Control for MIMO systems?

This is MRAC - Model Reference Adaptive Control for SISO systems. $G_m(s)$ is our reference model. It's is a first order system because they don't have overshoot. $G_m(s)$ is a desired wish how then ...
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Linear infinite optimization problem - when are KKT conditions sufficient for an optimum

I am trying to solve the following problem: $\max \int_0^T F(t, x(t)) dt$ s.t. $G(t,x(t)) \geq 0$ and $x(t) \in [0,1]$ for all $t\in[0,T]$ where F and G are smooth functions and affine in $x(t)$. (If ...
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Evaluate derivative of reachability Gramian: is this correct?

So I have the reachability Gramian matrix for a linear time-invariant system: \begin{align} W(t_{0},t) = \int_{t_{0}}^{t}e^{A(t-s)}BB^{\intercal}e^{A^{\intercal}(t-s)}. \end{align} In this case I have ...
Given the function: $\frac{s-5}{s^2-4s +5}$ The function have one zero and two poles in the RHP. So according to principle of argument (or Nyquist diagram), the Nyquist plot encircle the origin N = |Z-...