Dichotomy and absolute stability of nonlinear systems with periodically nonstationary linear part (Q1115840)

The author considers nonlinear systems of the form \[ \dot x(t)=A(t)x(t)+B(t)\cdot \xi (t,x(\cdot)|_{| o,t|}) \] where \(A(t)\in {\mathbb{R}}^{n\times n}\), \(B(t)\in {\mathbb{R}}^{n\times m}\) are periodic matrix functions and x(\(\cdot)\) and \(\xi\) (\(\cdot)\) satisfy a certain integral quadratic constraint. For these systems necessary and sufficient conditions for absolute stability and dichotomy are presented.