Domains of PID controller coefficients which guarantee stability and performance for LTI time-delay systems

In this work, the computation of the regions in the space of coefficients of a PID controller, inside which the controller stabilizes an LTI time-delay plant and guarantees a performance specification for the closed-loop system, is addressed. To ascertain the sensor noise attenuation, as a sample performance requirement, the H∞-norm of the weighted complementary sensitivity function is kept below a desired bound. The problem of minimization of the H∞-norm is transformed into the simultaneous stabilization of a family of quasipolynomials. Then, the stable domains of the PID coefficients are computed for these quasipolynomials using the parameter space approach. This work extends the previous results on the computation of the stability domains of a PID controller to ensure the desired performance specification for the closed-loop system.