7. Nonlinear Systems with Time-Variant Linear Parts

Abstract

Let us consider in Cⁿ the equation

$\displaystyle \dot x = A(t)x + F(x,t)\quad (t\geq 0), \quad\quad (1.1)$

where A(t) is a piecewise continuous Hurwitz n× n-matrix, and F maps $\Omega (r)\times [0, \infty)$ into Cⁿ. Recall that $\Omega (r) = \{h \in \mbox{C}^n : \parallel h\parallel \leq r\}$ for a positive number r.