Robust PIP Tracking Control for NMSS Models with Additive Nonlinear Dynamics and Noises: Discrete Time Cases

Compared with some other control system design strategies, such as GPC and LQG control, proportional-integral-plus (PIP) control for non-minimal state space (NMSS) systems is a flexible, logical approach to achieve control objectives for linear and near linear systems. In this paper, a generalized NMSS (GNMSS) model with additive nonlinear dynamics and input disturbances is considered instead of the classical linear NMSS system. For such GNMSS systems, the generalized peak-to-peak tracking control problem is considered by constructing a robust version of the PIP controller. Here the control objective is to guarantee, simultaneously, asymptotic stability, closed loop tracking performance, and attenuated peak-to-peak performance from the noise to the output of the nonlinear closed loop system. LMI-based solutions are developed to compute the parameters of the desired nonlinear PIP controller