Question: Consider the non-autonomous system --(1) where g() is continuously differentiable and satistics 0s g()skand g()s g(1)vt20. Taking V(x,.) = +(1+ g)) as a Lyapunov

Consider the non-autonomous system --(1) where g() is continuously differentiable and satistics

Consider the non-autonomous system --(1) where g() is continuously differentiable and satistics 0s g()skand g()s g(1)vt20. Taking V(x,.) = +(1+ g)) as a Lyapunov function candidate. Prove that the origin is uniformly asymptotically stable. Moreover, it is exponentially stable.

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