  In this paper we investigate a master-slave synchronization scheme of two
n-dimensional non-autonomous chaotic systems coupled by sinusoidal state error
feedback control, where parameter mismatch exists between the external harmonic
excitation of master system and that of slave one. A concept of synchronization
with error bound is introduced due to parameter mismatch, and then the bounds
of synchronization error are estimated analytically. Some synchronization
criteria are firstly obtained in the form of matrix inequalities by the
Lyapunov direct method, and then simplified into some algebraic inequalities by
the Gerschgorin disc theorem. The relationship between the estimated
synchronization error bound and system parameters reveals that the
synchronization error can be controlled as small as possible by increasing the
coupling strength or decreasing the magnitude of mismatch. A three-dimensional
gyrostat system is chosen as an example to verify the effectiveness of these
criteria, and the estimated synchronization error bounds are compared with the
numerical error bounds. Both the theoretical and numerical results show that
the present sinusoidal state error feedback control is effective for the
synchronization. Numerical examples verify that the present control is robust
against amplitude or phase mismatch.
