Many control systems must operate in two dimensions, for example, the x- and the y-axes. A two-axis control system is shown in Figure P3.10, where a set of state variables is identified. The gain of each axis is K1 and K2, respectively.

(a) Obtain the state differential equation.

(b) Find the characteristic equation from the A matrix.

(c) Determine the state transition matrix for K1 = 1 and K2 = 2.