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A closed form solution of the state space equations is easily obtained when the system matrix F is?

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A closed form solution of the state space equations is easily obtained when the system matrix F is?

(a) Transpose

(b) Symmetric

(c) Identity

(d) Diagonal

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This interesting question is from State-Space System Analysis and Structures topic in portion Discrete Time Systems Implementation of Digital Signal Processing

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Correct choice is (d) Diagonal

Easy explanation: A closed form solution of the state space equations is easily obtained when the system matrix F is diagonal. Hence, by finding a matrix P so that F^1=PFP^-1 is diagonal, the solution of the state equations is simplified considerably.

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