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Exponential filtering for uncertain Markovian jump time-delay systems with nonlinear disturbances
Copyright [2004] IEEE. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of Brunel University's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to [email protected]. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.In this paper, we study the robust exponential filter design problem for a class of uncertain time-delay systems with both Markovian jumping parameters and nonlinear disturbances. The jumping parameters considered here are generated from a continuous-time discrete-state homogeneous Markov process, and the parameter uncertainties appearing in the state and output equations are real, time dependent, and norm bounded. The time-delay and the nonlinear disturbances are assumed to be unknown. The purpose of the problem under investigation is to design a linear, delay-free, uncertainty-independent state estimator such that, for all admissible uncertainties as well as nonlinear disturbances, the dynamics of the estimation error is stochastically exponentially stable in the mean square, independent of the time delay. We address both the filtering analysis and synthesis issues, and show that the problem of exponential filtering for the class of uncertain time-delay jump systems with nonlinear disturbances can be solved in terms of the solutions to a set of linear (quadratic) matrix inequalities. A numerical example is exploited to demonstrate the usefulness of the developed theory
Control Design and Filtering for Wireless Networked Systems
This dissertation is concerned with estimation and control over wireless networked systems. Several problems are addressed, including estimator design over packet loss links, control and estimation over cognitive radio systems, modeling and prediction of wireless sensor networks (WSNs), and localization with the Theater Positioning System (TPS). The first problem addressed is the state estimation of a discrete-time system through a packet loss link modeled by a Bernoulli random variable. The optimal filter is derived by employing exact hybrid filtering. The performance of the optimal filter is illustrated by numerical simulations. Next, we consider the problem of estimation and control over cognitive radio (CR) systems. A two-switch model is first used to model this link. The linear optimal estimator and controller are derived over a single CR link. Also discussed here is estimation and control of the closed-loop system over two CR links. Furthermore, a more practical semi-Markov model for the CR system is proposed. Two cases are considered, where one assumes that acknowledgement of the information arrival is not available while the other assumes it is available. In the former, a suboptimal estimator is proposed and, in the latter, sufficient conditions are derived for the stability of a peak covariance process. Then, a controller design for the semi-Markov model is developed using linear matrix inequalities (LMIs). Additionally, the third problem addressed is modeling, identification, and prediction of the link quality of WSNs, such as the packet reception rate (PRR) and received signal strength indicator (RSSI). The state-space model is applied for this purpose. The prediction error minimization method (PEM) is employed for estimating parameters in the proposed model. The method employed is demonstrated through real measurements sampled by wireless motes. The last problem analyzed is localization using a new navigation system, TPS. In this study, we focus on users\u27 position estimation with the TPS when a GPS signal is not available. Several models are proposed to model transmission delays utilizing previous GPS signals. Last, a navigation scheme is provided for the TPS to improve its localization accuracy when the GPS signal is unavailable
Stability Analysis of Continuous-Time Switched Systems with a Random Switching Signal
This paper is concerned with the stability analysis of continuous-time
switched systems with a random switching signal. The switching signal manifests
its characteristics with that the dwell time in each subsystem consists of a
fixed part and a random part. The stochastic stability of such switched systems
is studied using a Lyapunov approach. A necessary and sufficient condition is
established in terms of linear matrix inequalities. The effect of the random
switching signal on system stability is illustrated by a numerical example and
the results coincide with our intuition.Comment: 6 pages, 6 figures, accepted by IEEE-TA
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