Stability conditions and Liapunov functions for quasi-polynomial systems

External Stability and Continuous Liapunov Functions

It is well known that external stability of nonlinear input systems can be investigated by means of a suitable extension of the Liapunov functions method. We prove that a complete characterization by means of continuous Liapunov functions is actually possible, provided that the de nition of external stability is appropriately strengthened.

Differential Inclusions and Monotonicity Conditions for Nonsmooth Liapunov Functions

In this paper we address the problem of characterizing the in nitesimal properties of functions which are non-increasing along all the trajectories of a di erential inclusion. In particular, we extend the condition based on the proximal gradient to the case of semicontinuous functions and Lipschitz continuous di erential inclusions. Moreover, we show that the same criterion applies also in the ...

Regularity of Liapunov Functions for Stable Systems

We consider the problem of characterizing those systems which admit (weak) Liapunov functions with nice analytic properties. Our investigation gives a rather complete picture of the situation for the one-dimensional case.

Time reparametrization and global stability of quasi-polynomial (QP) systems

Coupled systems of equations with entire and polynomial functions

We consider the coupled system$F(x,y)=G(x,y)=0$,where$$F(x, y)=bs 0 {m_1}   A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$.We    derive a priory estimates  for the sums of the rootsof the considered system andfor the counting function of  roots.