  Linear time invariant (LTI) systems are widely used for modeling system
dynamics in science and engineering problems. Harmonic oscillation of LTI
systems are widely used for modeling and analyses of periodic physical
phenomenon. This study investigates sufficient conditions to obtain harmonic
oscillation for high-order LTI systems. The paper presents a design procedure
for controlling harmonic oscillation of singleinput single-output high-order
LTI systems. LTI system coefficients are calculated by the solution of linear
equation set, which imposes a stable sinusoidal oscillation solution for the
characteristic polynomials of LTI systems. An example design is demonstrated
for fourth-order LTI systems and the control of harmonic oscillations are
discussed by illustrating Hilbert transform and spectrogram of oscillation
signals.
