522 research outputs found

    LMI based Stability and Stabilization of Second-order Linear Repetitive Processes

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    This paper develops new results on the stability and control of a class of linear repetitive processes described by a second-order matrix discrete or differential equation. These are developed by transformation of the secondorder dynamics to those of an equivalent first-order descriptor state-space model, thus avoiding the need to invert a possibly ill-conditioned leading coefficient matrix in the original model

    H∞ and H2 norms of 2D mixed continuous-discrete-time systems via rationally-dependent complex Lyapunov functions

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    This paper addresses the problem of determining the H∞ and H2 norms of 2-D mixed continuous-discrete-time systems. The first contribution is to propose a novel approach based on the use of complex Lyapunov functions with even rational parametric dependence, which searches for upper bounds on the sought norms via linear matrix inequalities (LMIs). The second contribution is to show that the upper bounds provided are nonconservative by using Lyapunov functions in the chosen class with sufficiently large degree. The third contribution is to provide conditions for establishing the tightness of the upper bounds. The fourth contribution is to show how the numerical complexity of the proposed approach can be significantly reduced by proposing a new necessary and sufficient LMI condition for establishing positive semidefiniteness of even Hermitian matrix polynomials. This result is also exploited to derive an improved necessary and sufficient LMI condition for establishing exponential stability of 2-D mixed continuous-discrete-time systems. Some numerical examples illustrate the proposed approach. It is worth remarking that nonconservative LMI methods for determining the H∞and H2 norms of 2-D mixed continuous-discrete-time systems have not been proposed yet in the literature.postprin

    Robust H∞ filtering for uncertain 2-D continuous systems

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    This paper considers the problem of robust H∞ filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H∞ norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H∞ filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method. © 2005 IEEE.published_or_final_versio

    H-infinity filtering with randomly occurring sensor saturations and missing measurements

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    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 H∞ filtering problem is investigated for a class of nonlinear systems with randomly occurring incomplete information. The considered incomplete information includes both the sensor saturations and the missing measurements. A new phenomenon of sensor saturation, namely, randomly occurring sensor saturation (ROSS), is put forward in order to better reflect the reality in a networked environment such as sensor networks. A novel sensor model is then established to account for both the ROSS and missing measurement in a unified representation by using two sets of Bernoulli distributed white sequences with known conditional probabilities. Based on this sensor model, a regional H∞ filter with a certain ellipsoid constraint is designed such that the filtering error dynamics is locally mean-square asymptotically stable and the H∞-norm requirement is satisfied. Note that the regional l2 gain filtering feature is specifically developed for the random saturation nonlinearity. The characterization of the desired filter gains is derived in terms of the solution to a convex optimization problem that can be easily solved by using the semi-definite program method. Finally, a simulation example is employed to show the effectiveness of the filtering scheme proposed in this paper.This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) of the UK under Grant GR/S27658/01, the Royal Society of the UK, the National Natural Science Foundation of China under Grants 61028008 and 60974030, the National 973 Program of China under Grant 2009CB320600, and the Alexander von Humboldt Foundation of Germany

    Towards Transient Growth Analysis and Design in Iterative Learning Control

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    In this article the problem of bounding transient growth in iterative learning control (ILC) is examined. While transient growth is not a desirable property, the alternative, robust monotonic convergence, leads to fundamental performance limitations. to circumvent these limitations, this article considers the possibility that some transient growth, if properly limited, is a viable and practical option. Towards this end, this article proposes tools for analysing worst-case transient growth in ILC. the proposed tools are based on pseudospectra analysis, which is extended to apply to ILC of uncertain systems. Two practical problems in norm-optimal ILC weighting parameter design are considered. Using the presented tools, it is demonstrated that successful design in the transient growth regime is possible, i.e. the transient growth is kept small while significantly improving asymptotic performance, despite model uncertainty
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