Control Systems...

Identify the matrix that can be a state transition matrix.

Let \(A = \left[ {\begin{array}{*{20}{c}} a&1\\ { - 3}&b \end{array}} \right]\) be system matrix of a system with characteristic equation s² + 5s + 3 = 0 then the value of a + b + ab is _________

Consider the following standard state-space description of a linear time-invariant single input single output system:

\(\dot x = Ax + Bu,y = Cx + Du\)

The system Ẋ = AX + Bu with \(A = \left[ {\begin{array}{*{20}{c}}{ - 1}&2\\0&2\end{array}} \right],\;B = \left[ {\begin{array}{*{20}{c}}0\\1\end{array}} \right]\) is

For the system,

\(\dot X = \left[ {\begin{array}{*{20}{c}} 2&0\\ 0&4 \end{array}} \right]X + \left[ {\begin{array}{*{20}{c}} 1\\ 1 \end{array}} \right]u\;;\;Y = \left[ {4\;0} \right]X,\)

With u as unit impulse and with zero initial state, the output y becomes 4e^at such that the value of a is _______

Given the homogenous state-space equation \(\dot x = \left[ {\begin{array}{*{20}{c}} { - 3}&1\\ 0&{ - 2} \end{array}} \right]x\). The steady-state value of \({x_{ss}} = \mathop {\lim }\limits_{t \to \infty } x\left( t \right)\), given the initial state value of x(0) = [10 - 10]^T is

A system is described by the dynamic equation ẋ(t) = A ⋅ x(t) + B ⋅ u(t), y(t) = C.x(t) where

\(A = \left[ {\begin{array}{*{20}{c}}{ - 1}&0\\0&{ - 2}\end{array}} \right],\;B = \left[ {\begin{array}{*{20}{c}}1\\0\end{array}} \right]\) and C = [1 1]