Consider the controller form of a single-input single-output linear system. 1 ... ... i(t) = x(t) + u(t) 1 -a0 -ai -An-1) 1 ... y(t) = (Bo B1 Bn-1) x(t) ... (a) Write down the transfer function H(s) = N(s) D(s) where N(s) is the numerator and D(s) is the denom- inator. (b) Suppose N(s) and D(s) are coprime, i.e., don't have a common factor other than 1, in which case the controller form is a minimal realization. Validate that D(s) = poles of a transfer function and eigenvalues of its associated realization are identical if the realization is minimal. det(sI – A). Discuss whether

The set of polynomials s a basis for IP2. Find the coordinate vector of elative to B. [p(t)]B = B = {3-4t,t−3+t²,− (7+7t+5t²)} p(t) = −3+(-2)t + 3t² in Cocalc). To solve this problem, you will at some point end up solving a system of linear equations; feel free to do that with a computer (e.g.,

Solve the system(calculus) [x, y, z] = [7, 2, -6] + s[2, 1, -3][x, y, z] = [3, 9, 13] + t[1, 5, 5]

A system of ordinary differential equations has an equilibrium point at the origin with the Jacobian matrix  J =  [0   1][-3  0]    what is the classification of the linearised system of equations at this equilibrium point? - Sink, centre, spiral source or star source?