The system is asymptotically stable in the large at the origin if :
A. It is stable
B. There exist a real number >0 such that || x (t0) || <=r
C. Every initial state x (t0) results in x (t) tends to zero as t tends to infinity
D. Both a and c
Answer:D
The system is asymptotically stable in the large at the origin if :
A. It is stable B. There exist a real number >0 such that || x (t0) || <=r C. Every initial state x (t0) results in x (t) tends to zero as t tends to infinity D. Both a and c
Explanation: By the definition of Liapunov’s stability criteria the system is asymptotically stable in the large 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.