Linear programming‐based proportional‐integral‐derivative control of positive systems

This paper investigates the proportional-integral-derivative (PID) control of positive systems in discrete-time case. First, a tuning parameter is introduced to construct framework systems. The problem thus transformed into synthesis with time-delay. By virtue matrix decomposition approach, gain matrices controller are designed. Using co-positive Lyapunov functions and linear programming, positivity stability achieved under designed controller. Then, reference signal solved. main contribution this lies that programming associated approach first presented handle Finally, two illustrative examples provided verify effectiveness proposed design.