A new PI-based optimal linear quadratic state-estimate tracker for discrete-time non-square non-minimum phase systems

A new proportional–integral (PI)-based optimal linear quadratic state-estimate tracker, derived using a proportional–integral–derivative (PID) filter-based frequency-domain shaping approach, is proposed in this paper for discrete-time non-square non-minimum phase multi-input-multi-output systems. Subsequently, a new integrated PID filter-shaped optimal PI state estimator is presented for the aforementioned systems, so that both the proposed state estimator and the state-estimate tracker are able to achieve satisfactory minimum phase-like tracking performance, for the case of arbitrary command inputs with significant variations at some isolated time instants.