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4. For an LTI discrete-time system Ck+1 = AIK (a) Use the quadratic Lyapunov function V(TK) = Ik with P = PT > 0 to derive the conditions for stability. In other words, you should obtain an equivalent of the algebraic Lyapunov equation that we derived in class for continuous-time systems. (b) Using the fact that, in continuous-time, the solution to the algebraic Lyapunov equation ATP + PA = -Q is given by P = $7 (t) Q D (t) dt where o(t) = est denotes the state-transition matrix, postulate how a solution to the algebraic Lyapunov equation in discrete-time should look like. Prove that your "guess" provides the unique solution to the algebraic Lyapunov equation