Duality of linear estimation for multiplicative noise systems with measurement delay

Abstract

This study firstly investigates the estimation problem for systems with multiplicative noise and measurement delay. Based on the innovation analysis approach, the estimators are developed in terms of a Riccati equation and a Lyapunov equation. The equations are of the same dimension as the plant; therefore compared with the augmentation approach, the presented approach lessens the computational demand. Then the linear quadratic regulation (LQR) problem for input delay systems is discussed based on non-augmented approach, and the controller is given in terms of a backward Riccati equation and a backward Lyapunov equation. Finally, the authors establish a duality between the estimation problem for measurement delay systems with multiplicative noise and the LQR problem for deterministic input delay systems with constraint conditions.