Can you solve a) and b) in matlab. Example : 10.3 State feedback control. Consider a time-invariant linear dynamical system with n-vector state xt and m-vector input ut , with dynamics xt+1 = Axt + But , t = 1, 2, . . . . The entries of the state often represent deviations of n quantities from their desired values, so xt ? 0 is a goal in operation of the system. The entries of the input ut are deviations from the standard or nominal values. For example, in an aircraft model, the states might be the deviation from the desired altitude, climb rate, speed, and angle of attack; the input ut represents changes in the control surface angles or engine thrust from their normal values. In state feedback control, the states are measured and the input is a linear function of the state, ut = Kxt . The m × n matrix K is called the state feedback gain matrix. The state feedback gain matrix is very carefully designed, using several methods. State feedback control is very widely used in many application areas (including, for example, control of airplanes). 30 (a) Open and closed-loop dynamical system. With ut = 0, the system satisfies xt+1 = Axt for t = 1, 2, . . ., which is called the open-loop dynamics. When ut = Kxt , the system dynamics can be expressed as xt+1 = Ax˜ t , for t = 1, 2, . . ., where the n × n matrix A˜ is the closed-loop dynamics matrix. Find an expression for A˜ in terms of A, B, and K.