Let (A,b,c) be a realization with A E Rx, b E R, and eR. Assume that...

Transcribed Image Text:

Let (A,b,c) be a realization with A E Rx, b E R", and eR". Assume that X, (4) + A, (4) #0 for all i, j. This assumption ensures the existence of XERX such that AX+XA + bc=0 Show that X is nonsingular if and only if (4.b) is controllable and (c. A) is observable. Let (A,b,c) be a realization with A E Rx, b E R", and eR". Assume that X, (4) + A, (4) #0 for all i, j. This assumption ensures the existence of XERX such that AX+XA + bc=0 Show that X is nonsingular if and only if (4.b) is controllable and (c. A) is observable.