controllability

A second-order linear time-invariant system is described by the following state equations $$$\eqalign{& {d \over {dt}}{x_1}\left( t \right) + 2{x_1}\left( t \right) = 3u\left( t \r...

Consider the system $${{dx} \over {dt}} = Ax + Bu$$ with $${\rm A} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right]\,\,\,and\,\,\,{\rm B} = \left[ {\matrix{ p \cr q \cr } } \righ...

The state variable equations of a system are: $$${\mathop {{x_1} = - 3{x_1} - x}\limits^ \bullet _2} + u$$$ $$${\mathop x\limits^ \bullet _2} = 2{x_1}$$$ $$$y = {x_1} + u.$$$ The s...

The system mode described by the state equations $$$X = \left( {\matrix{ 0 & 1 \cr 2 & { - 3} \cr } } \right)x + \left( {\matrix{ 0 \cr 1 \cr } } \right)u,y = \left[ {\matrix{ 1 &...

A linear time-invariant system is described by the state variable model $$$\left[ {\matrix{ {{{\mathop x\limits^ \bullet }_1}} \cr {{{\mathop x\limits^ \bullet }_2}} \cr } } \right...

A linear second order single input continuous-time system is described by the following set of differential equations $$$\eqalign{ & \mathop {{x_1}}\limits^ \bullet \left( t \right...