37 research outputs found
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Robust stability of two-dimensional uncertain discrete systems
Copyright [2003] 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 letter, We deal with the robust stability problem for linear two-dimensional (2-D) discrete time-invariant systems described by a 2-D local state-space (LSS) Fornasini-Marchesini (1989) second model. The class of systems under investigation involves parameter uncertainties that are assumed to be norm-bounded. We first focus on deriving the sufficient conditions under which the uncertain 2-D systems keep robustly asymptotically stable for all admissible parameter uncertainties. It is shown that the problem addressed can be recast to a convex optimization one characterized by linear matrix inequalities (LMIs), and therefore a numerically attractive LMI approach can be exploited to test the robust stability of the uncertain discrete-time 2-D systems. We further apply the obtained results to study the robust stability of perturbed 2-D digital filters with overflow nonlinearities
Finite-region boundedness and stabilization for 2D continuous-discrete systems in Roesser model
This paper investigates the finite-region boundedness (FRB) and stabilization problems for two-dimensional continuous-discrete linear Roesser models subject to two kinds of disturbances. For two-dimensional continuous-discrete system, we first put forward the concepts of finite-region stability and FRB. Then, by establishing special recursive formulas, sufficient conditions of FRB for two-dimensional continuous-discrete systems with two kinds of disturbances are formulated. Furthermore, we analyze the finite-region stabilization issues for the corresponding two-dimensional continuous-discrete systems and give generic sufficient conditions and sufficient conditions that can be verified by linear matrix inequalities for designing the state feedback controllers which ensure the closed-loop systems FRB. Finally, viable experimental results are demonstrated by illustrative examples
Robust synchronization for 2-D discrete-time coupled dynamical networks
This is the post-print version of the Article. The official published version can be accessed from the link below - Copyright @ 2012 IEEEIn this paper, a new synchronization problem is addressed for an array of 2-D coupled dynamical networks. The class of systems under investigation is described by the 2-D nonlinear state space model which is oriented from the well-known Fornasini–Marchesini second model. For such a new 2-D complex network model, both the network dynamics and the couplings evolve in two independent directions. A new synchronization concept is put forward to account for the phenomenon that the propagations of all 2-D dynamical networks are synchronized in two directions with influence from the coupling strength. The purpose of the problem addressed is to first derive sufficient conditions ensuring the global synchronization and then extend the obtained results to more general cases where the system matrices contain either the norm-bounded or the polytopic parameter uncertainties. An energy-like quadratic function is developed, together with the intensive use of the Kronecker product, to establish the easy-to-verify conditions under which the addressed 2-D complex network model achieves global synchronization. Finally, a numerical example is given to illustrate the theoretical results and the effectiveness of the proposed synchronization scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61028008 and 61174136, the International Science and Technology Cooperation Project of China under
Grant No. 2009DFA32050, the Natural Science Foundation of Jiangsu Province of China under Grant BK2011598, the Qing Lan Project of Jiangsu Province of China, the Project sponsored by SRF for ROCS of SEM 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
Stability analysis and control design for 2-D fuzzy systems via basis-dependent Lyapunov functions
This paper investigates the problem of stability analysis and stabilization for two-dimensional (2-D) discrete fuzzy systems. The 2-D fuzzy system model is established based on the Fornasini-Marchesini local state-space model, and a control design procedure is proposed based on a relaxed approach in which basis-dependent Lyapunov functions are used. First, nonquadratic stability conditions are derived by means of linear matrix inequality (LMI) technique. Then, by introducing an additional instrumental matrix variable, the stabilization problem for 2-D fuzzy systems is addressed, with LMI conditions obtained for the existence of stabilizing controllers. Finally, the effectiveness and advantages of the proposed design methods based on basis-dependent Lyapunov functions are shown via two examples. © 2011 The Author(s).published_or_final_versionSpringer Open Choice, 28 May 201
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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)
H∞ control for 2-D time-delay systems with randomly occurring nonlinearities under sensor saturation and missing measurements
In this paper, the H∞ output-feedback control problem is investigated for a class of two-dimensional (2-D) nonlinear systems with time-varying delays under imperfect measurements. Randomly occurring nonlinearities (RONs) are introduced in the system to account for probabilistic nonlinear disturbances typically caused by networked environments and governed by a sequence of random variables obeying the Bernoulli distribution. The imperfect measurement outputs are subject to both data missing and randomly occurring sensor saturations (ROSSs), which are put forward to characterize the network-induced phenomena such as probabilistic communication failures and limited capacity of the communication devices. The aim of this paper is to design an output-feedback controller such that the closed-loop system is globally asymptotically stable in the mean square and the prescribed H∞ performance index is satisfied. Sufficient conditions are presented by resorting to intensive stochastic analysis and matrix inequality techniques, which not only guarantee the existence of the desired controllers for all possible time-delays, RONs, missing measurements and ROSSs but also lead to the explicit expressions of such controllers. Finally, a numerical simulation example is given to demonstrate the applicability of the proposed control scheme.This work was supported in part by the National Natural Science Foundation of China under Grants 61174136, 61134009 and 61329301, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the “333 Project” Foundation of Jiangsu Province, the Programme for New Century Excellent Talents in University under Grant NCET-12-0117, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
Stability and Robust Stability of 2D Discrete Stochastic Systems
New stability and robust stability results are given based on weaker conservative assumptions. First, new boundary
condition is designed. It is less conservative and has broader application range than that has been given. Then,
we derive the results which have the same form, but under a weaker conservative assumption. Meanwhile, the process of the proofs has been simplified. Finally, an example is given to illustrate our results. Our results can be extended to the fields of stabilization, filtering and state estimation, and so forth
LMI Conditions for Robust Stability of 2D Linear Discrete-Time Systems
Robust stability conditions are derived for uncertain 2D linear discrete-time systems, described by Fornasini-Marchesini second models with polytopic uncertainty. Robust stability is guaranteed by the existence of a parameter-dependent Lyapunov function obtained from the feasibility of a set of linear matrix inequalities, formulated at the vertices of the uncertainty polytope. Several examples are presented to illustrate the results
Distributed H ∞ state estimation for stochastic delayed 2-D systems with randomly varying nonlinearities over saturated sensor networks
In this paper, the distributed H ∞ state estimation problem is investigated for the two-dimensional (2-D) time-delay systems. The target plant is characterized by the generalized Fornasini-Marchesini 2-D equations where both stochastic disturbances and randomly varying nonlinearities (RVNs) are considered. The sensor measurement outputs are subject to saturation restrictions due to the physical limitations of the sensors. Based on the available measurement outputs from each individual sensor and its neighboring sensors, the main purpose of this paper is to design distributed state estimators such that not only the states of the target plant are estimated but also the prescribed H ∞ disturbance attenuation performance is guaranteed. By defining an energy-like function and utilizing the stochastic analysis as well as the inequality techniques, sufficient conditions are established under which the augmented estimation error system is globally asymptotically stable in the mean square and the prescribed H ∞ performance index is satisfied. Furthermore, the explicit expressions of the individual estimators are also derived. Finally, numerical example is exploited to demonstrate the effectiveness of the results obtained in this paper