Consider the linear differential equation of n-th order where T > ˆ 0 and a0,...,an−1 ∈ R are given constants. The control u is assumed to be an L∞([0, Tˆ]) function. Show that the system of linear...

Consider the linear differential equation of n-th order

where T > ˆ 0 and a0,...,an−1 ∈ R are given constants. The control u

is assumed to be an L∞([0, Tˆ]) function. Show that the system of linear

differential equations of first order which is equivalent to this differential

equation of n-th order satisfies the Kalman condition.