PROJECT TITLE :

An Asymptotic Ratio Characterization of Input-to-State Stability

ABSTRACT:

For continuous-time nonlinear systems with inputs, we tend to introduce the notion of an asymptotic ratio input-to-state stability (ISS) Lyapunov operate. The spinoff of such a perform along solutions is upper-bounded by the distinction of two terms whose ratio is asymptotically smaller than 1 for large states. This asymptotic ratio condition is generally a lot of convenient to test than commonplace ISS Lyapunov function conditions. We have a tendency to show that the existence of an asymptotic ratio ISS Lyapunov perform is cherish ISS. A related notion of ISS with nonuniform convergence rate is also explored.