Reference tracking in sampled-data systems: a DLMI-based purely-discrete PID framework

This paper presents a tracking reference design condition based on a purely discrete-time PID controller aimed at sampled-data linear systems operating over hybrid time domains. The proposed method formulates the PID tuning problem as a convex optimization task based on Differential Linear Matrix Inequalities (DLMIs), with the specific objective of minimizing the H2 guaranteed cost of the tracking error signal. Purely discrete PID gains are obtained automatically without requiring model reduction or transformation to continuous-time domains. The resulting controller ensures stability and performance by imposing an H2 upper limit cost for hybrid systems. Numerical examples are used to show the effectiveness and practicality of the proposed method.