Stability of Linear Volterra-Stieltjes Differential Equations
SIAM Journal on Control and Optimization
| Hi-index | 0.00 |
An explicit criterion for positivity of the solution semigroup of linear Volterra integro-differential systems with infinitely many delays is given. Then exponential asymptotic stability is studied, and it is shown that, roughly speaking, a linear Volterra integro-differential system with delay is exponentially asymptotically stable if its characteristic equation has no zeros in the closed right half complex plane and the “kernel part” of the system exponentially decays. In particular, some simple criteria for exponential asymptotic stability of positive systems are presented. Finally, two sufficient conditions for exponential asymptotic stability of positive systems subjected to structured perturbations and affine perturbations are given. A simple example is given to illustrate the obtained results.