Structured observer-based controller for delayed systems with two unstable poles and minimum phase zeros.

This paper analyses the problem of control and stabilization of a particular class of Linear Time Invariant (LTI) systems. The system under consideration has two unstable poles, n real stable poles, m minimum phase zeros plus time delay. An observer based controller with four tunable gains is proposed as a control strategy in order to ensure a stable behaviour of the closed-loop system. Sufficient conditions for the existence of the proposed scheme are obtained in terms of the upper limit of time delay size and the poles and zeros position. The controller parameters are tuned using a non-smooth H∞ optimization method. The proposed control strategy is applied to an unstable linearized model of a continuously stirred tank reactor (CSTR) in order to show the effectiveness of the proposed design scheme. Numerical results are presented.