1.

The system is asymptotically stable at the origin if :(a) It is stable(b) There exist a real number >0 such that || x (t0) ||

Answer»

The correct option is (d) It is unstable

To ELABORATE: By the DEFINITION of Liapunov’s stability criteria the system is asymptotically STABLE at the origin if there exist a real number >0 such that || X (t0) || <=r and every initial state x (t0) results in x (t) TENDS to zero as t tends to infinity .



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