Linear Framework on PID Control of Continuous-Time Positive Systems

Abstract

This paper establishes a linear framework on the proportional-integral-differentiation (PID) control of continuous-time positive systems (CTPSs). An improved PID controller is proposed for CTPSs by introducing a small parameter. A matrix decomposition approach is presented to describe the PID controller gains. A dependent derivative part design of PID controller is used to reduce the effect of inverse matrix on the systems. Using copositive Lyapunov function (CLF), the positivity and stability of the resulting closed-loop systems is achieved under the designed PID controller. The obtained approach is developed for the systems with reference signal. All conditions are solvable via linear programming (LP). The novelties of the paper lie in that: (i) An LP-based PID framework is constructed for CTPSs, (ii) A matrix decomposition approach is presented to design the derivative part dependently, and (iii) The PID design framework can be developed for other issues of CTPSs.