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Transverse problem in coaxial regions leads to the well known Bessel equation. Solution of this equation is in the form of Fourier-Bessel expansion of which eigenvalues are determined by the appropriate transcendental equations. In electromagnetics, two symmetric cases: Dirchlet-Dirichlet (D-D) and Neumann-Neumann (N-N) are fundamental both from practical and theoretical points of view. The first...
This paper deals with the three-dimensional Autoregressive (3-D AR) model parameter estimation from noisy data. We develop an algorithm to estimate the transversal AR parameters corresponding to the Quarter-Space (QS) region of support without a priori knowledge of additive noise power. The transversal parameters and the noise variance are both obtained as a solution of a quadratic eigenvalue problem...
Deterministic finite state automata can be modelled within the framework of the boolean differential calculus. One way back to conventional arithmetics leads to multi-linear discrete models of the automata. There the escrow issue is that even if state feedback is applied, in general the models still remain nonlinear. The method presented here is to embed the nonlinear state space within a linear state...
A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are discussed. An overview of applications which have so far received interest are given and some potential application areas remaining to be explored are noted.
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.
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...
In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use...
Solving unstructured linear differential-algebraic equations in the presence of numeric uncertainty in the equation coefficients is an ill-posed problem — arbitrarily small changes in the coefficients of the leading matrix may change the solution completely. To obtain well-posedness, assumptions must be made, even for DAE of index 0. In this work, we propose assumptions about the system poles to obtain...
In this paper we study certain infinite-dimensional Sylvester equations. The equations are closely related to robust output regulation of infinite-dimensional systems. If the signal generator is finite-dimensional or has discrete spectrum and a complete set of orthonormal eigenvectors, there are some known sufficient conditions for the decomposing of these Sylvester equations. In this paper we generalize...
There are significant incentives in controlling the end-use properties in batch reactors to reduce the variability in the final product quality specifications. Here we define an approach for controlling the properties within a desired target region, instead of a set point, with an economic objective and with consideration of the model uncertainty. The approach to handling process-model mismatch is...
The fact that the feedback interconnection of strictly positive real (spr) systems leads to an asymptotically stable closed loop can be used for the synthesis of robust observer-based state-space controllers. Since most control plants originally are not spr structural modifications must be done to establish this property even under parameter variations. Going that way one gets a modified spr plant...
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...
This paper considers the problem of applying eigenstracture assignment to parameter dependant systems. The concept of modal sensitivity is introduced, and a recently presented method for the assignment of reduced sensitivity eigenstracture is presented in this context. A new proof for this method is presented, allowing greater insight into the sensitivity problem, and leading to a more flexible design...
The eigenvector structure necessary to achieve good short term attitude command response in a generic single rotor helicopter are presented. They achieve appropriate mode decoupling and are consistent with the physical relationships between the state variables. These eigenvectors translate exactly into ideal transfer functions for use with a variety of control design methodologies.
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.
This paper is concerned with the application of eigenstracture assignment to nonlinear systems. Conventionally, eigenstracture assignment considers only a single operating point during design, and as a result may produce a controller that is sensitive to plant parameter variations. Here, the eigenvector subspace is considered to produce a controller that takes account of two operating conditions,...
This paper addresses the n-vehicle formation shape maintenance problem in the plane. The objective is to design decentralized motion control laws for each vehicle to restore formation shape in the presence of small perturbations from the desired shape. Formation shape is restored by actively controlling a certain set of interagent distances, and we assign the task of controlling a particular interagent...
The goal of this paper is the analysis of the dynamic behavior of a multi-phase asynchronous motor. The Power-Oriented Graphs technique has been used for modeling the system and a very simple and compact model has been obtained. The steady-state equations of the system have been studied finding remarkable relations between the motor voltage and current vectors. The eigenvalues of the electrical part...
In this work we present a new algorithm to solve the average-consensus problem. The main goal of this algorithm is to obtain exact convergence despite the existence of quantized communication channels between the agents. Starting from the Zoom-in Zoom-out strategy already presented in [5], we introduce the equations describing the behaviour of the algorithm and we formally prove the asymptotic agreement...
Complex-fractional systems are systems that are governed by a differential equation characterized by complex order fractional derivatives. A new modeling tool is proposed and used to study these systems: complex order state-space representation. The tool results from the extension of the differentiation order, from order 1 to complex order, in the state equation of classical state-space representation:...
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