# Questions tagged [linear-control]

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

290 questions
6 views

### existence of solution of wave equation with a feedback term

If we have a system of coupled wave equations with a feedback acting on one equation,that is $u_{tt}-\Delta u+py-\alpha(t)d^{2}(x)u_{t} =0$ $y_{tt}-\Delta y+pu=0$ $u=y=0$ on boundary $\Gamma$ with d ...
32 views

### How can I design a (PID) Controller if I don't have a reference signal?

I have been trying to control lateral and longitudinal movement of a robot for an autonomous lane keeper project. I have no problem with the lateral movement, however I couldn2t figure out exactly how ...
21 views

### Model reduction of estimated state space models - System identification

Assume that we have a dynamical model in form of this simple transfer function $$G(s) = \frac{1}{2s^2 + 5s + 4}$$ G = tf(1, [2 5 4]) We do a step response with ...
32 views

### How can I reduce noise from measurement without a Kalman Filter?

I'm going to create an adaptive Model Predictive Controller (MPC). The model is a state space model. Due to noise, it's very difficult to determine the model order. I'm using subspace identification ...
7 views

### the system controllability and observability

If a linear system is controllable, does it mean we can find the control standard form in state space, but it doesn't mean all the forms of state space representations is controllable?
46 views

25 views

### Why the angle is $-180°$ at $\omega = 0$ for this system

I'm trying to plot the nyquist from the analytical expression of the system but the bode plot generated by matlab yields an angle -180 whereas the analytical expression yields zero when $\omega=0$. ...
49 views

### Exosystem for reference generation

Recently I have read a paper where an LTI system of the form \begin{align} \dot{x}_p &= A_p x_p + B_p u \\ y &= C_p x_p \end{align}\tag{1} for the control plant was considered. In ...
36 views

### Questions about LQG with full information

I have implemented LQG in MATLAB software. But, now I do not know how to determine the value of optimal cost. Each way of calculating cost, returns a different value. Which one should I trust to ...
53 views

### Show that if a linear dynamical equation is controllable at $t_0$, then it is controllable at any $t<t_0$.

Consider a $n$-dimentional $p$-input equation: $$\dot{x}=Ax+Bu$$ where $A$ and $B$ are constant $n\times n$ and $n\times p$ real matrices. By definition, the latter state equation is said to be ...
56 views

34 views

51 views

66 views

27 views

### from multi input to single input in linear dynamical systems

I am working with some linear multi input dynamical systems. There is a result here which reduces the problem to single input linear systems. Given the following linear system:  \dot{X} = A\cdot X + ...
106 views

Which of the systems are Lyapunov, asymptotically or BIBO stable: $1) \quad \left[ \begin{array}{c|c} A & B\\ \hline C & \end{array} \right]=\left[ \begin{array}{ccc|c} -2&1&0&2\\ ... 1answer 94 views ### Stability of Discrete Time state space system with eigenvalues 0, 1/2 and 1. This question is from a system theory exam without answers. So I was wondering if my resoning is correct. Consider the discrete-time state-space realization$x(t+1)=Ax(t)+Bu(t), \quad y(t)=Cx(t), \...
Consider the continuous-time state-space representation $\frac{d}{dt}x(t)=Ax(t)+Bu(t), \quad y(t)=Cx(t), \quad t \in R^+,$ with the matrices given by \$A =\begin{bmatrix}-4&-5&0&5\\-4&...