E3.13 A system is described by the two differential equations

where w1t2 and y1t2 are functions of time, and u1t2 is an input.

(a) Select a set of state variables.

(b) Write the matrix differential equation and specify the elements of the matrices.

(c) Find the characteristic roots of the system in terms of the parameters a and b.

dy(t) +y(t) 2u(t) + aw(t) = 0, dt