Differential Equations and Linear Algebra, 6.2: Diagonalizing a Matrix

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Differential Equations and Linear Algebra, 6.2: Diagonalizing a Matrix

Problem 2. (Repeated eigenvalues) Consider the SISO LTI systemx = Ax Bu, y = Cx Du,x ∈ℝ^n, u, y ∈ℝ^1.(a) Assume that A is a diagonal matrix and B, C are column/row vectors with entries bi and ci,respectively. Write the controllability and observability matrices for this system.(b) Show that if A is a diagonal matrix with repeated eigenvalues, then the pair (A, B) cannot becontrollable and the pair (A, C) cannot be observable.(c) Can you find a SISO minimal realization for which the mat

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