WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 17, 2018
Exponential Stability of Nonautonomous Infinite Dimensional Systems
Author:
Abstract: Let H be a Hilbert space with the unit operator I. We consider linear non-autonomous distributed parameter systems governed by the equation dy/dt = S(t)y + B(t)y (y = y(t), t > 0), where S(t) is an unbounded operator, such that for some constant c, S(t)+cI is dissipative; B(t) is an operator uniformly bounded on [0,∞), having a uniformly bounded derivative and commuting with S(t). Exponential stability conditions are established. An illustrative example is presented.