Robust multivariable PID control for linear parameter varying systems

Practical control problems often deal with uncertain systems depending on parametric and possibly time-varying uncertainties. Quadratic stability theory and recent advances in convex and nonconvex optimisation algorithms provide useful tools to cope with this kind of problems. On the other hand, PID is still the controller most commonly used for industrial problems. In this paper, we consider a certain class of Multi input-multi output linear parameter varying systems which are encountered in practical control problems and we propose a state space parameterisation which allows to convert PI and PID controller synthesis into an LMI or BMI optimisation problem. The proposed technique guarantees uniform exponential stability of the closed loop system, a desired rate of convergence, and an H∞ norm bound. © 2001 Elsevier Science Ltd. All rights reserved.