If V is positive definite, and dV/dx is negative definite, then zero state is asymtotically stable.
If V is positive definite and dV/dx is negative semi-definite, then zero state is stable, but may not be asymtotically stable.
Here is where the invariant set theorem comes into play, and it is also where I am quite unclear about. (assuming x-> zero state as t -> infinity)
Which statements are correct? Or are all of them incorrect?
1) If the largest invariant set includes ONLY the zero state, then it is asymtotically stable.
2) If the largest invariant set includes zero state plus other states, then it is only stable.
3) If the largest invariant set doesn't include the zero state, then it is only stable.
Anyone?
If V is positive definite and dV/dx is negative semi-definite, then zero state is stable, but may not be asymtotically stable.
Here is where the invariant set theorem comes into play, and it is also where I am quite unclear about. (assuming x-> zero state as t -> infinity)
Which statements are correct? Or are all of them incorrect?
1) If the largest invariant set includes ONLY the zero state, then it is asymtotically stable.
2) If the largest invariant set includes zero state plus other states, then it is only stable.
3) If the largest invariant set doesn't include the zero state, then it is only stable.
Anyone?
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