$H_{\infty}$ Fixed-Interval Smoothing Estimation for Time-Delay Systems

Abstract

This paper is concerned with the fixed-interval smoothing estimation for time-delay systems which include continuous-time case and discrete-time case. In the case of discrete-time systems, the problem can be solved by using the conventional state augmentation approach. However, this approach is not suitable for the continuous-time case. In this paper, we will propose a unified approach to study the fixed-interval smoothing problem for both continuous-time and discrete-time systems with output delays. By introducing a suitable stochastic linear time-delay models in an indefinite space, it is shown that the fixed-interval smoother can be obtained by calculating fixed-interval smoother for time-delay systems in an indefinite space. Therefore, based on the orthogonal projection theory in an indefinite space, the fixed-interval smoothers for time-delay systems are designed by performing Riccati equations with the same dimension as the original systems. Moreover, a necessary and sufficient conditions for the existence of the fixed-interval smoother will also be given.

A Bayesian robust Kalman smoothing framework for state-space models with uncertain noise statistics

“…Kalman smoothing is an offline signal processing tool where both past and future observations are used for making estimations [22][23][24][25][26][27][28][29]. Kalman smoothers can be classified as fixed-point, fixed-lag, and fixed-interval smoothers [30]; however, the term Kalman smoother generally refers to the fixed-interval case in which the goal is to estimate the sequence of states over a finite time window using all observations in the same window.…”