Consider the system is described in state variable form by x(0 = Ax(/) + B(f) y(t) =

Chapter 0, Problem DP9.10

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Consider the system is described in state variable form by x(0 = Ax(/) + B(f) y(t) = Cx(r) where A - 0 1 L 2 3 ,B = "o" [lj [1 0]. Assume that the input is a linear combination of the states, that is, u(t) = -Kx(r) + r(f), where r{t) is the reference input and the gain matrix is K = [K\ K2]. Substituting u(t) into the state variable equation yields the closed-loop system x(0 = [A - BK]x(0 + Br(/) y{t) = Cx(/) (a) Obtain the characteristic equation associated withA-BK. (b) Design the gain matrix K to meet the following specifications: (i) the closed-loop system is stable; (ii) the system bandwidth