A delay-dependent approach to H∞ filtering for stochastic delayed jumping systems with sensor non-linearities

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Taylor & Francis Ltd.In this paper, a delay-dependent approach is developed to deal with the stochastic H∞ filtering problem for a class of It type stochastic time-delay jumping systems subject to both the sensor non-linearities and the exogenous non-linear disturbances. The time delays enter into the system states, the sensor non-linearities and the external non-linear disturbances. The purpose of the addressed filtering problem is to seek an H∞ filter such that, in the simultaneous presence of non-linear disturbances, sensor non-linearity as well as Markovian jumping parameters, the filtering error dynamics for the stochastic time-delay system is stochastically stable with a guaranteed disturbance rejection attenuation level γ. By using It's differential formula and the Lyapunov stability theory, we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist. These conditions are dependent on the length of the time delay. We then characterize the expression of the filter parameters, and use a simulation example to demonstrate the effectiveness of the proposed results.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Nuffield Foundation of the U.K.under Grant NAL/00630/G, and the Alexander von Humboldt Foundation of Germany

Robust filtering for stochastic genetic regulatory networks with time-varying delay

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper addresses the robust filtering problem for a class of linear genetic regulatory networks (GRNs) with stochastic disturbances, parameter uncertainties and time delays. The parameter uncertainties are assumed to reside in a polytopic region, the stochastic disturbance is state-dependent described by a scalar Brownian motion, and the time-varying delays enter into both the translation process and the feedback regulation process. We aim to estimate the true concentrations of mRNA and protein by designing a linear filter such that, for all admissible time delays, stochastic disturbances as well as polytopic uncertainties, the augmented state estimation dynamics is exponentially mean square stable with an expected decay rate. A delay-dependent linear matrix inequality (LMI) approach is first developed to derive sufficient conditions that guarantee the exponential stability of the augmented dynamics, and then the filter gains are parameterized in terms of the solution to a set of LMIs. Note that LMIs can be easily solved by using standard software packages. A simulation example is exploited in order to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Biotechnology and Biological Sciences Research Council (BBSRC) of the U.K. under Grants BB/C506264/1 and 100/EGM17735, an International Joint Project sponsored by the Royal Society of the U.K., the Research Grants Council of Hong Kong under Grant HKU 7031/06P, the National Natural Science Foundation of China under Grant 60804028, and the Alexander von Humboldt Foundation of Germany

Observer-based networked control for continuous-time systems with random sensor delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the networked control system design for continuous-time systems with random measurement, where the measurement channel is assumed to subject to random sensor delay. A design scheme for the observer-based output feedback controller is proposed to render the closed-loop networked system exponentially mean-square stable with H∞ performance requirement. The technique employed is based on appropriate delay systems approach combined with a matrix variable decoupling technique. The design method is fulfilled through solving linear matrix inequalities. A numerical example is used to verify the effectiveness and the merits of the present results.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor George Yin under the direction of Editor Ian R. Petersen. This work was supported in part by the Royal Society of the UK, the National Natural Science Foundation of China (60774047, 60674055) and the Taishan Scholar Programs Foundation of Shandong Province, China

Filtering for uncertain 2-D discrete systems with state delays

This is the post print version of the article. The official published version can be obtained from the link below - Copyright 2007 Elsevier Ltd.This paper is concerned with the problem of robust H∞ filtering for two-dimensional (2-D) discrete systems with time-delays in states. The 2-D systems under consideration are described in terms of the well-known Fornasini–Marchesini local state-space (FMLSS) models with time-delays. Our attention is focused on the design of a full-order filter such that the filtering error system is guaranteed to be asymptotically stable with a prescribed H∞ disturbance attenuation performance. Sufficient conditions for the existence of desired filters are established by using a linear matrix inequality (LMI) approach, and the corresponding filter design problem is then cast into a convex optimization problem that can be efficiently solved by resorting to some standard numerical software. Furthermore, the obtained results are extended to more general cases where the system matrices contain either polytopic or norm-bounded parameter uncertainties. A simulation example is provided to illustrate the effectiveness of the proposed design method.This work was partially supported by the National Natural Science Foundation of China (60504008), Program for New Century Excellent Talents in University of China and the Postdoctoral Science Foundation of China (20060390231)

Probability-dependent gain-scheduled filtering for stochastic systems with missing measurements

Copyright @ 2011 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.This brief addresses the gain-scheduled filtering problem for a class of discrete-time systems with missing measurements, nonlinear disturbances, and external stochastic noise. The missing-measurement phenomenon is assumed to occur in a random way, and the missing probability is time-varying with securable upper and lower bounds that can be measured in real time. The multiplicative noise is a state-dependent scalar Gaussian white-noise sequence with known variance. The addressed gain-scheduled filtering problem is concerned with the design of a filter such that, for the admissible random missing measurements, nonlinear parameters, and external noise disturbances, the error dynamics is exponentially mean-square stable. The desired filter is equipped with time-varying gains based primarily on the time-varying missing probability and is therefore less conservative than the traditional filter with fixed gains. It is shown that the filter parameters can be derived in terms of the measurable probability via the semidefinite program method.This work was supported in part by the Leverhulme Trust of the U.K., the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the National Natural Science Foundation of China under Grants 61028008, 61074016 and 60974030, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, and the Alexander von Humboldt Foundation of Germany

Robust H∞ filtering for discrete nonlinear stochastic systems with time-varying delay

This is the postprint version of the article. The official published version can be accessed from the link below - © 2007 Elsevier IncIn this paper, we are concerned with the robust H∞ filtering problem for a class of nonlinear discrete time-delay stochastic systems. The system under study involves parameter uncertainties, stochastic disturbances, time-varying delays and sector-like nonlinearities. The problem addressed is the design of a full-order filter such that, for all admissible uncertainties, nonlinearities and time delays, the dynamics of the filtering error is constrained to be robustly asymptotically stable in the mean square, and a prescribed H∞ disturbance rejection attenuation level is also guaranteed. By using the Lyapunov stability theory and some new techniques, sufficient conditions are first established to ensure the existence of the desired filtering parameters. These conditions are dependent on the lower and upper bounds of the time-varying delays. Then, the explicit expression of the desired filter gains is described in terms of the solution to a linear matrix inequality (LMI). Finally, a numerical example is exploited to show the usefulness of the results derived.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Nuffield Foundation of the UK under Grant NAL/00630/G, the Alexander von Humboldt Foundation of Germany, the National Natural Science Foundation of China (60774073 and 10471119), the NSF of Jiangsu Province of China (BK2007075 and BK2006064), the Natural Science Foundation of Jiangsu Education Committee of China under Grant 06KJD110206, and the Scientific Innovation Fund of Yangzhou University of China under Grant 2006CXJ002

Robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process

This paper investigates the problem of robust L2 - L∞ filtering for a class of dynamical systems with nonhomogeneous Markov jump process. The time-varying transition probabilities which evolve as a nonhomogeneous jump process are described by a polytope, and parameter-dependent and mode-dependent Lyapunov function is constructed for such system, and then a robust L2 -L8 filter is designed which guarantees that the resulting error dynamic system is robustly stochasticallystable and satisfies a prescribed L2 - L∞ performance index. A numerical example is given to illustrate the effectiveness of the developed techniques

Robust H∞ control for a class of nonlinear stochastic systems with mixed time delay

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2007 Wiley-Blackwell LtdThis paper is concerned with the problem of robust H∞ control for a class of uncertain nonlinear Itô-type stochastic systems with mixed time delays. The parameter uncertainties are assumed to be norm bounded, the mixed time delays comprise both the discrete and distributed delays, and the sector nonlinearities appear in both the system states and delayed states. The problem addressed is the design of a linear state feedback controller such that, in the simultaneous presence of parameter uncertainties, system nonlinearities and mixed time delays, the resulting closed-loop system is asymptotically stable in the mean square and also achieves a prescribed H∞ disturbance rejection attenuation level. By using the Lyapunov stability theory and the Itô differential rule, some new techniques are developed to derive the sufficient conditions guaranteeing the existence of the desired feedback controllers. A unified linear matrix inequality is proposed to deal with the problem under consideration and a numerical example is exploited to show the usefulness of the results obtained.This work was funded by the Engineering and Physical Sciences Research Council Grant Number: GR/S27658/01, Nuffield Foundation. Grant Number: NAL/00630/G, Alexander von Humboldt Foundation, National Natural Science Foundation of Jiangsu Education Committee of China Grant Number: 06KJD110206, National Natural Science Foundation Grant Numbers: 10471119, 10671172, Scientific Innovation Fund of Yangzhou University of China. Grant Number: 2006CXJ002

A novel approach to fault detection for fuzzy stochastic systems with nonhomogeneous processes

In this paper, we consider a class of fuzzy stochastic systems with nonhomogeneous jump processes. Our focus is on the design of a fuzzy fault detection filter that is sensitive to faults but robust against unknown inputs. Furthermore, the error filtering system is stochastically stable. With reference to an H1 performance index and a new performance index, sufficient conditions to ensure the existence of a fuzzy robust fault detection filter are derived. Simulation studies are carried out, showing that the proposed fuzzy robust FD filter can rapidly detect the faults correctly