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

Reliable H∞ filtering for discrete time-delay systems with randomly occurred nonlinearities via delay-partitioning method

The official published version can be found at the link below.In this paper, the reliable H∞ filtering problem is investigated for a class of uncertain discrete time-delay systems with randomly occurred nonlinearities (RONs) and sensor failures. RONs are introduced to model a class of sector-like nonlinearities that occur in a probabilistic way according to a Bernoulli distributed white sequence with a known conditional probability. The failures of sensors are quantified by a variable varying in a given interval. The time-varying delay is unknown with given lower and upper bounds. The aim of the addressed reliable H∞ filtering problem is to design a filter such that, for all possible sensor failures, RONs, time-delays as well as admissible parameter uncertainties, the filtering error dynamics is asymptotically mean-square stable and also achieves a prescribed H∞ performance level. Sufficient conditions for the existence of such a filter are obtained by using a new Lyapunov–Krasovskii functional and delay-partitioning technique. The filter gains are characterized in terms of the solution to a set of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the proposed design approach

Probability-guaranteed H∞ finite-horizon filtering for a class of nonlinear time-varying systems with sensor saturations

This is the Post-Print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 ElsevierIn this paper, the probability-guaranteed H∞ finite-horizon filtering problem is investigated for a class of nonlinear time-varying systems with uncertain parameters and sensor saturations. The system matrices are functions of mutually independent stochastic variables that obey uniform distributions over known finite ranges. Attention is focused on the construction of a time-varying filter such that the prescribed H∞ performance requirement can be guaranteed with probability constraint. By using the difference linear matrix inequalities (DLMIs) approach, sufficient conditions are established to guarantee the desired performance of the designed finite-horizon filter. The time-varying filter gains can be obtained in terms of the feasible solutions of a set of DLMIs that can be recursively solved by using the semi-definite programming method. A computational algorithm is specifically developed for the addressed probability-guaranteed H∞ finite-horizon filtering problem. Finally, a simulation example is given to illustrate the effectiveness of the proposed filtering scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008, 60825303 and 60834003, National 973 Project under Grant 2009CB320600, the Fok Ying Tung Education Fund under Grant 111064, the Special Fund for the Author of National Excellent Doctoral Dissertation of China under Grant 2007B4, the Key Laboratory of Integrated Automation for the Process Industry (Northeastern University) from the Ministry of Education of China, the Engineering and Physical Sciences Research Council (EPSRC) of the U.K. under Grant GR/S27658/01, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

Non-fragile H∞ control with randomly occurring gain variations, distributed delays and channel fadings

This study is concerned with the non-fragile H∞ control problem for a class of discrete-time systems subject to randomly occurring gain variations (ROGVs), channel fadings and infinite-distributed delays. A new stochastic phenomenon (ROGVs), which is governed by a sequence of random variables with a certain probabilistic distribution, is put forward to better reflect the reality of the randomly occurring fluctuation of controller gains implemented in networked environments. A modified stochastic Rice fading model is then exploited to account for both channel fadings and random time-delays in a unified representation. The channel coefficients are a set of mutually independent random variables which abide by any (not necessarily Gaussian) probability density function on [0, 1]. Attention is focused on the analysis and design of a non-fragile H∞ outputfeedback controller such that the closed-loop control system is stochastically stable with a prescribed H∞ performance. Through intensive stochastic analysis, sufficient conditions are established for the desired stochastic stability and H∞ disturbance attenuation, and the addressed non-fragile control problem is then recast as a convex optimisation problem solvable via the semidefinite programme method. An example is finally provided to demonstrate the effectiveness of the proposed design method

Probability-dependent gain-scheduled control for discrete stochastic delayed systems with randomly occurring nonlinearities

This is the post-print version of the Article. The official published version can be accessed from the links below - Copyright @ 2012 John Wiley & Sons, Ltd.In this paper, the gain-scheduled control problem is addressed by using probability-dependent Lyapunov functions for a class of discrete-time stochastic delayed systems with randomly occurring sector nonlinearities. The sector nonlinearities are assumed to occur according to a time-varying Bernoulli distribution with measurable probability in real time. The multiplicative noises are given by means of a scalar Gaussian white noise sequence with known variances. The aim of the addressed gain-scheduled control problem is to design a controller with scheduled gains such that, for the admissible randomly occurring nonlinearities, time delays and external noise disturbances, the closed-loop system is exponentially mean-square stable. Note that the designed gain-scheduled controller is based on the measured time-varying probability and is therefore less conservative than the conventional controller with constant gains. It is shown that the time-varying controller gains can be derived in terms of the measurable probability by solving a convex optimization problem via the semi-definite programme method. A simulation example is exploited to illustrate the effectiveness of the proposed design procedures.This work was supported in part by the Leverhulme Trust of the UK, the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the National Natural Science Foundation of China under Grants 61028008, 61134009, 61074016, 61104125 and 60974030, the Shanghai Natural Science Foundation of China under Grant 10ZR1421200, 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

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