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In this paper, the generalized Lyapunov equation approach is used to study stochastic stabilization/detectability with state-multiplicative noise. Some practical test criteria for stochastic stabilization and detectability, such as stochastic Popov--Belevitch--Hautus Criterion for exact detectability, are obtained. Moreover, useful properties of the generalized Lyapunov equation are derived based on critical stability and exact detectability introduced in this paper. As applications, first, the stochastic linear quadratic regulator as well as the related generalized algebraic Riccati equation are discussed extensively. Second, the infinite horizon stochastic [H.sub.2]/[H.sub.[infinity]] control with state- and control-dependent noise is also investigated, which extends and improves the recently published results. Index Terms--Exact detectability, generalized algebraic Riccati equation (GARE), spectrum, stabilization, stochastic linear quadratic regulator, [H.sub.2]/[H.sub.[infinity]] control.

This paper considers the problem of robust channel estimation for direct-sequence code-division multiple-access (DS-CDMA) systems with time-varying multipath fading channels. Due to the lack of accurate knowledge of model dynamics and statistics of system noises, a polynomial H[infinity] channel estimator is developed by virtue of the Krein space theory. The estimator is calculated by performing a J-spectral factorization. In this paper, under some conditions, we obtain a closed-form solution to this J-spectral factorization, which greatly reduces the computational load of the estimator design. The simulation results show that the proposed H[infinity] estimator provides a robust estimation performance against various types of noises and modeling errors. Index Terms--Direct-sequence code-division multiple access (DS-CDMA), H[infinity] channel estimation, multipath fading channels, polynomial approach, robustness.

This brief is concerned with robust Kalman filtering for linear discrete-time systems with both instantaneous and single delayed measurements. The norm-bounded parameter uncertainties enter into the system matrix of the state space model. A new approach through the re-organization of measurements is proposed to improve the efficiency of computation. A sufficient condition for the existence of a robust Kalman filter is derived. The performance is clearly demonstrated through analytical results and simulation experiments. Index Terms--Discrete systems, Kalman filters, robustness, single delay.

This paper proposes and analyzes a new distributed power-control algorithm based on the theory of stochastic approximation. The power-control problem is first converted into a stochastic approximation problem in which the zero point of a specific function is determined. A distributed power-control algorithm is then derived and its convergence properties are analyzed using standard techniques. In the distributed algorithm, each user iteratively updates its power level by using estimates of the inverse of the signal-to-interference ratio (SIR) of its channel. No knowledge of the channel gains or state information of other users is required. Moreover, the algorithm is robust in the sense that it can handle errors in the bit-error rate estimates, and hence, can be used in practical scenarios. Convergence of the algorithm is analyzed in the almost-sure sense. Index Terms--Decentralized control, power control, stochastic approximation, time-varying systems.

This paper is concerned with the finite horizon [H.sub.[infinity]] full-information control for discrete-time systems with multiple control and exogenous input delays. We first establish a duality between the [H.sub.[infinity]] full-information control and the [H.sub.2] smoothing of a stochastic backward system in Krein space. Like the duality between the llinear quadratic regulation (LQR) of linear systems without delays and the Kalman filtering, the established duality allows us to address complicated multiple input delay problems in a simple way. Indeed, by applying innovation analysis and standard projection in Krein space, in this paper we derive conditions under which the [H.sub.[infinity]] full-information control is solvable. An explicit controller is constructed in terms of two standard Riccati difference equations of the same order as the original plant (ignoring the delays). As special cases, solutions to the [H.sub.[infinity]] state feedback control problem for systems with delays only in control inputs and the [H.sub.[infinity]] control with preview are obtained. An example is given to demonstrate the effectiveness of the proposed [H.sub.[infinity]] control design. Index Terms--Discrete-time system, [H.sub.[infinity]] control, multiple input delays, Riccati difference equation, smoothing estimation.

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.

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

A new and simple approach to optimal recursive filtering, prediction, and smoothing for singular stochastic discrete-time systems is presented by using a time-domain innovation analysis method. The estimators are calculated based on an ARMA innovation model which can be obtained using spectral factorization or a recursive identifier. The prediction problem for the singular systems is solved with the aid of an output predictor. Further, a simple solution is presented for the complex smoothing problem. Index Terms--Discrete-time systems, optimal state estimation, stochastic singular systems, time-domain innovation analysis method.