Proportional-Derivative Control of Discrete-Time Positive Systems: A State-Space Approach

The proportional-derivative (PD) control is investigated for discrete-time positive linear systems in this paper, which is a fundamental research problem in positive systems theory. Based on positive systems theory and Lyapunov theory, this paper proposes a systematic approach on the PD controller design for positive stabilization. The analyses and methods presented in this paper preserve both the necessity and sufficiency of the control problem, and the convergence of the algorithm is also analyzed. Finally, a numerical example on pest population control is employed in the simulation to verify the results.