# Questions tagged [linear-systems]

The tag has no usage guidance.

10 questions
Filter by
Sorted by
Tagged with
19 views

### Is it possible to calculate Over Shoot percentage and settling time of an Underdamped 2nd order system with Ramp input?

Most of the books derive Over Shoot percentage, settling time for 2nd order underdamped it for unit step response. Do these parameters exist for 2nd order underdamped system for Ramp response too? If ...
39 views

### Quality of the transient response for an arbitrary transfer function

The question is simple and I rather need a reference point. How the parameters of transients are estimated (as in the picture) from an arbitrary linear transfer function (formula is given).
27 views

### Linear Nastran model not converging

I am running a SOL 101 linear statics FEA. If I fix down the whole geometry it converges. But anything less than around 90% fix down and it will sit there crunching away at the numbers forever. This ...
43 views

### Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x

I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system. i.e. $$\dot{x}(t) = Ax(t)$$ is stable ...
40 views

### LQR control effort / control bandwidth relationship

I'm working with a linear system, having given matrices A and B $$A = \left[\begin{array}{cc} 0 & 1 \\ -0.9 & 0 \end{array}\right]$$ $$B = \left[\begin{array}{c} 0 \\ 2 \end{array}\right]$$ ...
34 views

### Feedback Control Question: Finding compensator numerator (B(s)) and denominator (A(s)) polynomials to satisfy a specific requirement

I wish to find the polynomials B(s) and A(s) in the following compensator equation: A(s)D(s) + B(s)N(s) = F(s) Given, $$N(s) = s - 2$$ $$D(s) = s^2 - 1$$ $$F(s) = s^2 + 3*s + 4$$ Condition The degree ...
I want to make a kalman filter that will estimate the upwash coefficient $C_{\alpha_{up}}$ my state vector: $X_k=[u \ v \ w \ C_{\alpha_{up}} ]^T$ My measurement vector: $Z_k =[\alpha_m \ \beta_m ... 1answer 312 views ### Why is it impossible to create an observer for this not fully observable system? Consider a 1D point-mass moving along an axis. A force$u\$ is applied as control. There is no gravity or other forces involved. The system can be described in state space equations as: \begin{align}... 2answers 246 views ### Controllability of x' = Ax + Bu(t) implies controllability of \left \{ \begin{matrix} x' = Ax + By \\ y'=u(t) \end{matrix} \right. Suppose that the systemx'(t)=Ax(t)+Bu(t)$$is controllable in \mathbb{R}^n, where A is n \times n, B is  n \times m and u(t) is m \times 1 Show that the system$$\left \{ \begin{...
Given the following system: $$\dot{x} = \begin{bmatrix}1 & 1 & 0 \\ 0 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}x + \begin{bmatrix}0 & 1 \\ 1 & 0 \\ 0 & 1 \end{bmatrix} u$$...