Abstract
This paper proposes novel fractional cosine and sine matrix
functions derived from a determining matrix. It introduces a new
controllability criterion based on the controllability Gramian for
achieving exact controllability in oscillating fractional linear systems
with damping term. We present Cayley-Hamilton type theorem for
determining matrix. Finally, we prove a novel Kalman type rank criterion
for controllability in oscillating fractional linear systems with
damping, which is a novel contribution even in systems without damping.
Numerical examples are provided to validate these findings.
