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The Radial Basis Function method (RBF) can be used not only for reconstruction of a surface from scattered data but for reconstruction of damaged images, filling gaps and for restoring missing data in images, too. The basic idea of reconstruction algorithm with RBF and very interesting results from reconstruction of images damaged by noise are presented. Feasibility of the RBF method for image processing...
This article presents a statistical analysis of the Matrix Pencil method for estimating the mode and the amplitude of a single damped complex exponential. This study is based on a perturbation analysis of the mode and the amplitude, assuming a high signal-to-noise ratio. Closed-form expressions of the mean and variance of these perturbations are derived. It is shown that the estimates are unbiased...
The paper presents a small gain result for systems with jumps. As an application of this result, a state-feedback robust, stabilisation problem with respect, to parametric uncertainty of sampled-data systems is considered. A numerical example illustrates the theoretical developments.
The aim of this paper is to investigate some properties of the solutions of the differential Riccati-type systems arising in control problems for the time-varying linear systems with jumps. A major attention is paid to the stabilising solution of these systems. Necessary and sufficient conditions for the existence of such solution are derived in the time-invariant case.
The robustness of discrete iterative learning controller a-gainst initial state state error for discrete-time plant is investigated in this paper. When the initial state remains fixed for each iteration but is different from the desired one, it is shown that the output will converge to a trajectory which is the same as the desired one except the initial point for a traditional D-type discrete iterative...
Necessary and sufficient conditions are given for multiple input discrete-time linear systems to be controllable where the inputs are constrained to be greater than some negative values. Furthermore a simple method to test the controllability with input constraints is proposed by using the Jordan canonical form and constructing some particular form of input matrices based on the elimination method...
This paper is concerned with the selection of optimal Laguerre bases for the orthonormal series expansion of discrete-time Volterra models. The aim is to minimize the number of functions needed to provide a given approximation accuracy, thus simplifying the modeling and control problems associated with these models. This issue was addressed by Fu and Dumont [8] focusing on linear systems, which are...
In this article we present, in a tutorial fashion, an introduction to the links between flatness, generalized PID control and sliding mode control of linear systems. Several simple illustrative examples are presented including computer simulations and experimental results.
A class of complex control systems, modelled as a finite family of stochastic differential equations with state-dependent noise is considered. Each individual equation of this family describes the plant state variable in individual regime of the system composed of a set of interconnected subsystems. The transitions between these regimes are discontinuous and are modelled by a homogeneous Markov chain...
A simple, unified formulation for the solution of the entire eigenstructure assignment problem by output feedback is proposed. This is obtained by using a matrix transformation similar to that of the matrix pencils. Furthermore, this formulation may result in a more simple partial eigenstructure solution; as shown in the paper, for an n-order linear system with m inputs and r outputs, r eigenstructure...
In this paper we show that for linear systems there is a strong relation between P.O.D. approximation and balanced truncation. Using this relation we obtain an error estimate for the P.O.D. approximation in the Hoc-norm. A small Hoc-norm is needed in order to guarantee that a controller design for the reduced system will perform well on the original system.
Moment matching approach of model reduction of linear dynamical state-space systems for a given input-generating system is discussed and applied to port-Hamiltonian systems. It is shown that the reduced order models inherit the port-Hamiltonian structure, the passivity property and preserve a certain number of the moments of a transfer function. Another approach to model reduction of port-Hamiltonian...
This paper deals with the robust control of an Autonomous Underwater Vehicle (AUV), using the ℋ∞ approach for Linear Parameter Varying (LPV) polytopic systems. This method seems to be adapted to this kind of system because of the important non-linearities and the uncertainties on the hydrodynamics parameters. After the presentation of the nonlinear model of the AUV considered for the study, an LPV...
This paper deals with the stability of a class of Markov Jump Linear Systems characterized by piecewise-constant transition rates and system dynamics. These systems are called Switching Markov Jump Linear Systems. Mean square stability analysis is carried out by studying the time evolution of the second-order moment of the state. A sufficient condition guaranteeing mean square stability under constraints...
Some proofs concerning a subspace identification algorithm are presented. It is proved that the Kalman filter gain and the noise innovations process can be identified directly from known input and output data without explicitly solving the Riccati equation. Furthermore, it is in general and for colored inputs, proved that the subspace identification of the states only is possible if the deterministic...
The fractional differintegration problem is treated from the Signal Processing point of view. A brief review of the Laplace transform approach to differintegration is done. The continuous-time/discrete-time system conversion is discussed and presented a Grünwald-Letnikov integration.
The concept of frequency weighted balancing, as proposed by Enns, is a generalization of internally balanced model truncation. Internally balanced truncation is simple to apply and additionally attractive because of the existence of an upper _ffœ error bound that is a function of the neglected Hankel singular values. A conjecture on the generalization of this upper error bound for the case of frequency...
Typical digital implementations of feedback controllers periodically measure the state, compute the control law, and update the actuators. Although periodicity simplifies the analysis and implementation, it results in a conservative usage of resources. In this paper we drop the periodicity assumption in favor of self-trigger strategies that decide when to measure the state, execute the controller,...
This work considers the problem of stabilization of first order linear systems subject to a relatively large input-output time delay. As it is known, the stability analysis of this type of systems becomes difficult due to the dead-time term involved. The proposed prediction scheme has a similar structure of a Smith predictor scheme together with a output injection compensation to guarantee predictor...
We consider here the problem of finding a controller for a system such that when interconnected to the plant, we get a system which is bisimilar to the desired system. We give necessary and sufficient conditions for the existence of such a controller. The systems we consider are ordinary linear time invariant dynamical systems described by state space equations. We briefly compare our results with...
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