# GATE Questions & Answers of State Space Model, State Transition Matrix

## What is the Weightage of State Space Model, State Transition Matrix in GATE Exam?

Total 2 Questions have been asked from State Space Model, State Transition Matrix topic of Control Systems subject in previous GATE papers. Average marks 1.50.

In the signal flow diagram given in the figure, ${u}_{1}$ and ${u}_{2}$ are possible inputs whereas ${y}_{1}$ and ${y}_{2}$ are possible outputs. When would the SISO system derived from this diagram be controllable and observable?

$\left[\begin{array}{c}\stackrel{.}{{x}_{1}}\\ \stackrel{.}{{x}_{2}}\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\left[\begin{array}{c}{x}_{1}\\ {x}_{2}\end{array}\right]+\left[\begin{array}{c}1\\ 1\end{array}\right]u$