Stability investigations and exponential estimations for functional differential equations of retarded type (Q802844)

The author applies a Lyapunov functional of the form \[ V(t,\phi)=\phi^ T(0)\phi (0)+\int^{0}_{-r}\phi^ T(s)U(t+s)\phi (s)ds, \] where \(\phi\in C\), U: [-r,\(\infty)\to {\mathbb{R}}^{n\times n}\) is a continuous, positive semidefinite matrix function, to obtain some exponential estimates for solutions of the functional differential equation \(\dot x(t)=A(t,x_ t)x(t)+B(t,x_ t)x(t-r)\) where A and B are certain matrix functionals.