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This note focuses on the traditional problem of the Kalman filtering for linear continuous-time systems. Although the problem has been studied widely in the past decades, little work has been done for the time-delayed systems and some fundamental problems remain to be solved. This note proposes a new tool, namely, reorganization innovation analysis approach, to investigate the filtering problem for systems with delayed measurements. The Kalman filter is given in terms of the solution of standard Riccati equations. The performance is clearly demonstrated through analytical results and simulation. The solved problem in this note is related with some more complicated problems such as H[infinity] fixed-lag smoothing, H[infinity] control with preview and control with input delays. Index Terms--Continuous-time system, Kalman filter, reorganized innovation analysis, Riccati equations, time-delayed systems.

This paper deals with a class of power control problems where the system link gains are assumed to be time varying and the signal-to-interference ratio (SIR) estimates are allowed to be corrupted with bounded noises. A simple control algorithm is devised by applying a distributed, fixed step approach. It is a feedback algorithm that requires only local information. By modifying the distributed, fixed step power control algorithm proposed by Sung and Wong, we obtain here a more robust version that can handle time varying link gains and measurement noises. The convergence property of the new algorithm is established and simulation studies were carried out to show that it is effective. Index Terms--Cellular mobile system, distributed algorithm, power control, time-varying channels.

This note studies the finite horizon H[infinity] fixed-lag smoothing problem for linear continuous time-varying systems. A new technique named as reorganized innovation analysis in Krein space is developed to give a necessary and sufficient condition for the existence of an H[infinity] fixed-lag smoother. The condition is given in terms of the boundedness of two matrix functions which are derived from the solutions of two Riccati differential equations (RDEs), one standard H[infinity] filtering RDE and one [H.sub.2] type of RDE. Examples demonstrate the proposed H[infinity] fixed-lag smoother design and the fact that the existence of an H[infinity] smoother does not depend on the solvability of H[infinity] filtering. Index Terms--Continuous-time systems, H[infinity] fixed-lag smoothing, innovation analysis, Krein space, Riccati equation.

This note will address a linear minimum variance estimation of discrete-time systems with instantaneous and delayed measurements. Although the problem may be approached via system augmentation and standard Kalman filtering, the computation of filter may be expensive when the dimension of the system is high and the measurement lag is significant. In this note, a new tool, termed as reorganized innovation sequence, is presented for deriving the optimal filter. The optimal filter is given by two Riccati difference equations (RDEs) with the same dimension as that of the original system. The approach is shown to induce saving of computational cost us compared to the system augmentation approach, especially when the delay is large. Further, it can be extended to solving the more complicated [H.sub.[infinity]] fixed-lag smoothing in Krein space. Index Terms--Delayed measurement, discrete-time systems, innovation analysis, optimal filtering, Riccati equations.

In this paper, we aim to solve the long-standing [H.sub.[infinity]] fixed-lag smoothing problem for time-varying continuous systems. By applying a novel innovation analysis approach in an indefinite linear space, a sufficient and necessary condition for the existence of an [H.sub.[infinity]] fixed-lag smoother is derived. The [H.sub.[infinity]] smoother is calculated by performing the linear matrix differential equation and the integral equation. Index Terms--Continuous-time systems, fixed-lag smoothing, [H.sub.[infinity]], innovation approach, time varying.

This paper is concerned with the optimal steady-state estimation for singular stochastic discrete-time systems using a polynomial equation approach. The key to the optimal estimation is the calculation of an optimal estimator gain matrix. The main contribution of the paper is the derivation of a simple method for computing the gain matrix. Our method involves solving one simple polynomial equation which is derived from the uniqueness of the autoregressive moving average (ARMA) innovation model. The approach covers prediction, filtering, and smoothing problems. Further, when the noise statistics of the model are not available, self-tuning estimation is performed by identifying one ARMA innovation model. Index Terms--Innovation analysis, optimal state estimation, polynomial equation approach, self-tuning estimation, singular stochastic systems.

This paper studies optimal control and stabilization problems for continuous‐time mean‐field systems with input delay, which are the fundamental development of control and stabilization problems for mean‐field systems. There are two main contributions: (1) To the best of the authors' knowledge, the present paper is the first to establish the necessary and sufficient solvability condition for this kind of optimal control problem with input delay, and to derive the analytical form of an optimal controller through overcoming the obstacle that separation principle no longer holds for multiplicative‐noise systems. (2) For the stabilization problem, under the assumption of exact observability, it is strictly proven that the system is stabilizable if and only if the algebraic Riccati equation has a unique positive definite solution. [ABSTRACT FROM AUTHOR]

In standard linear-quadratic (LQ) control, the first step in investigating infinite-horizon optimal control is to derive the stabilisation condition with the optimal LQ controller. This paper focuses on the stabilisation of an Itô stochastic system with indefinite control and state-weighting matrices in the cost functional. A generalised algebraic Riccati equation (GARE) is obtained via the convergence of the generalised differential Riccati equation (GDRE) in the finite-horizon case. More importantly, the necessary and sufficient stabilisation conditions for indefinite stochastic control are obtained. One of the key techniques is that the solution of the GARE is decomposed into a positive semi-definite matrix that satisfies the singular algebraic Riccati equation (SARE) and a constant matrix that is an element of the set satisfying certain linear matrix inequality conditions. Using the equivalence between the GARE and SARE, we reduce the stabilisation of the general indefinite case to that of the definite case, in which the stabilisation is studied using a Lyapunov functional defined by the optimal cost functional subject to the SARE. [ABSTRACT FROM AUTHOR]

Research into the infinite horizon deconvolution for discrete time-variant systems is presented.