ABSTRACT
State-estimation forms an integral part of control systems theory. Estimating the state-variables of a dynamic model is important to help in improving our knowledge about different systems for the purpose of analysis and control design. The celebrated Kalman filtering algorithm [3,4] is the optimal estimator over all possible linear ones and gives unbiased estimates of the unknown state vectors under the conditions that the system and measurement noise processes are mutually-independent Gaussian distributions. Robust state-estimation arises out of the desire to estimate unmeasurable state variables when the plant model has uncertain parameters. In [17], a Kalman filtering approach has been studied with an H∞-norm constraint. For systems with bounded parameter uncertainty, the robust estimation problem has been addressed in [11,12,32]. Despite the frequent occurence of uncertain systems with state-delay in engineering applications, the problem of estimating the state of an uncertain system with state-delay has been overlooked. The purpose of this chapter is to consider the state-estimation problem for linear systems with norm-bounded parameter uncertainties and unknown state-delay. SpecificaJly, we address the state-estimator design problem such that the estimation error covariance has a guaranteed bound for all admissible uncertainties and state-delay. We will divide efforts into two parts: one part for contiouous-time systems and the other part for discrete-time systems. Both time-varying and steady-state robust Kalman filtering are considered. The main tool for solving the foregoing problem is the Riccati equation approach and the end result is an extended robust Kalman filter the solution of which is expressed in terms of two Riccati equations involving scaling parameters.
