When will the linear system x ax be asymptotically or marginally stable?

1. How do you determine if a system is asymptotically stable?
2. How do you know if a system is marginally stable?
3. Is asymptotically stable same as marginally stable?
4. What is asymptotically stable?

How do you determine if a system is asymptotically stable?

If V (x) is positive definite and (x) is negative semi-definite, then the origin is stable. 2. If V (x) is positive definite and (x) is negative definite, then the origin is asymptotically stable.

How do you know if a system is marginally stable?

A marginally stable system is one that, if given an impulse of finite magnitude as input, will not "blow up" and give an unbounded output, but neither will the output return to zero. A bounded offset or oscillations in the output will persist indefinitely, and so there will in general be no final steady-state output.

Is asymptotically stable same as marginally stable?

A system is marginally stable iff all eigenvalues of A have magnitudes less than or equal to 1 and those with unity magnitude are simple roots of the minimal polynomial of A. A system is asymptotically stable iff all s of A have magnitudes less than 1.

What is asymptotically stable?

Asymptotic stability means that solutions that start close enough not only remain close enough but also eventually converge to the equilibrium. Exponential stability means that solutions not only converge, but in fact converge faster than or at least as fast as a particular known rate .