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We propose a decomposition framework for the parallel optimization of the sum of a differentiable (possibly nonconvex) function and a (block) separable nonsmooth, convex one. The latter term is usually employed to enforce structure in the solution, typically sparsity. Our framework is very flexible and includes both fully parallel Jacobi schemes and Gauss–Seidel (i.e., sequential) ones, as well as...
In this paper is proposed a method to characterize a Time-Frequency Representation (TFR). This characterization takes place in a process which aim is to extract spectral patterns of an uni-dimensional signal from its TFR. The originality of this method is that the Time-Frequency plane is considered from a local point of view. Statistical features of set of TFR coefficients are defined in order to...
The problem of non-conservative minimisation of the maximum amplitude of error signals in the time domain for multivariable systems subject to uncertain inputs is considered. It is shown that this problem, which is usually tackled using L1 control theory, can also be addressed in the framework of H∞ theory, via the introduction of some new signal uncertainty sets, and a slight modification of the...
In this paper a new morphological technique suitable for colour image skeleton extraction is presented. Vector morphological operations are defined by means of a new ordering of vectors of the HSV colour space, which is a combination of conditional and partial sub-ordering. Then, these are used to extract skeletons of colour images in terms of erosions and openings. The proposed method was tested...
The corrected Field of View (FoV) in Adaptive Optics (AO) is limited by the anisoplanatism effect. Multi-Conjugate AO (MCAO) aims at providing a wide FoV correction through the use of several Deformable Mirrors (DMs) and of multi-guide-star WaveFront Sensor (WFS). However the performance optimization of such complex systems raises new questions in terms of calibration and control. We present our current...
We study hybrid systems from a global geometric perspective as piecewise smooth dynamical systems. Based on an earlier work, we define the notion of the hybrifold as a single piece-wise smooth state space reflecting the dynamics of the original system. Structural stability for hybrid systems is introduced and analyzed in this framework. In particular, it is shown that a Zeno state is locally structurally...
A new method is proposed for the solution of linear matrix inequalities over a finite horizon for linear discrete time varying systems with or without uncertainties. The method is used to solve a variety of problems beginning with the standard H∞ discrete-time bounded real lemma and extending through to robust H∞ general-filtering and output-feedback control design of uncertain systems. In the latter...
This paper proposes a new structure for the classical median vector filter. It is based on a vector ordering relation obtained by associating a cumulative distance to each vector. The specifity of the proposed filter relies in the definition of the neighboring window used to calculate this distance. The filter presents both an enhancement and a registration effect, combined with a smoothing effect...
This paper presents a novel Virtual Reality tool for visualising image neighbourhoods. It is currently implemented using RGB colour space, but the technique is not limited to Cartesian spaces. The Visualisation Tool is based on Virtual Reality Modeling Language (VRML). Visualisation using virtual reality techniques is a useful tool to help evaluate the effectiveness of colour filters. It can also...
Nowadays, there is not a low delay audio coding standard that achieves nearly-transparent quality. The ISO-MPEG standards are profusely used in audio for high quality coding. They use perceptual models that require high frequency resolution. In applications where the delay is a critical parameter, i.e. when the use of a feedback channel is important, the ISO-MPEG algorithms are not suitable. In this...
We consider interconnected nonlinear systems with external inputs. Each of the subsystems is assumed to be input-to-state stable (ISS). Sufficient conditions of small-gain type are provided guaranteeing that the interconnection is ISS. To this end we extend recently obtained small gain theorems to a more general type of interconnections. The small gain theorem proved here is applicable to situations...
In this report a new algorithm is presented for the spectral factorization of a two-sided symmetric polynomial. The method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques, namely the famous fast Fourier transform routine (FFT), brings high computational efficiency and reliability. The power of the proposed procedure...
The objective of this work is to solve the problem of fast dynamics which appears in the synthesis of LPV controllers using a single quadratic Lyapunov function. This can be a serious problem for controller implementation or computer simulation. The solution is achieved by means of an extra LMI added to the set of LMI's used to design the controller. This LMI defines the region where the poles of...
In this talk we solve the problem of the title. Compared to earlier work we give a fast and direct algorithm for the computation of the transfer operators of the discrete Cauchy problem over general submonoids of Zr instead of Nr and also consider the case of convergent solutions. For the latter situation we use ideas of C. Riquier [1910!].
The paper considers stability of periodic solutions in a class of periodically forced nonlinear systems depending on a scalar parameter and subject to disturbances. The stability analysis — based on a combined use of linearization techniques and frequency-domain stability criteria expressed via Integral Quadratic Constraints — can be efficiently performed in terms of Linear Matrix Inequalities. An...
Suppose a nonlinear plant is stabilized by a nonlinear controller, and further assume that the plant is unknown but the controller is known. Suppose also that the use of a new controller appears attractive. This paper extends our results for linear time-invariant systems and proposes novel nonlinear analysis results, utilizing the kernel representation of nonlinear systems, for ensuring that the introduction...
This paper proposes a novel model predictive control (MPC) scheme based on multiobjective optimization. At each sampling time, the MPC control action is chosen among the set of Pareto optimal solutions based on a time-varying and state-dependent decision criterion. After recasting the optimization problem associated with the multiobjective MPC controller as a multiparametric multiobjective linear...
This paper develops a necessary and sufficient condition for the following relationship to exist between two given uncertain systems defined in terms of IQCs: Every input-output behaviour of the first uncertain system is an input-output behaviour of the second uncertain system.
Hypercomplex 2D Fourier transforms have been proposed by several authors with applications in image processing of both grayscale and colour images. Previously published works on hypercomplex Fourier transforms have utilized direct evaluation of a Fast Fourier transform using hypercomplex arithmetic. This paper shows that such transforms may be implemented by decomposition into two independent complex...
Spatial discretisation of fluid mechanical systems typically leads to descriptor systems consisting of large numbers of differential algebraic equations (DAEs). In an effort to apply standard control theory to such systems, physical insight is often used to analytically reformulate the DAE as an ordinary differential equation (ODE). In general, this is a difficult process that typically requires expert...
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