Observer Design for Time-delay Systems

The paper presents the design of an observer for a general class of systems with delays in states (retarded systems). A state space model of observer with delays is proposed. The novelty of the study is to include the state derivatives in the design. The stability of the observer is proved by Lyapunov approach. Linear Matrix Inequality (LMI) approach is used in the analysis of the problem. To design observer we use simple Luenberger approach, but we introduced here two feedback lines instead of one. The first feedback line contains a proportional gain matrix(L1) and second feedback line has a gain matrix (L2) (given) followed by a differentiator block. So here we are considering not only the difference between real states and estimator states or error signals but also the rate of change of error signals. It is claimed that taking into consideration both error and rate of change of error data would make the observer more reliable than a simple Luenberger type. Finally, at the end of the book some numerical examples are studied in order to demonstrate the validity of the approach.