1,721,876 research outputs found
Some results on robust stability of discrete time systems
No full textThe theorem of Kharitonov on the Hurwitz property of interval families of polynomials cannot be extended, in genera, to obtain sufficient conditions for the stability of families of characteristic polynomials of discrete-time systems. Necessary and sufficient conditions for this stability problem are given. Such conditions naturally give rise to a computationally efficient stability test which requires the solution of a one-parameter optimization problem and which can be considered as a counterpart to the Kharitonov test for continuous-time systems. At the same time, the method used to derive the stability conditions provides a procedure for solving another stability robustness problem, i.e. the estimation of the largest domain of stability with a rectangular box shape around given nominal values of the polynomial coefficients
Robustness of pole location in perturbed systems
No full textIn this paper we present some results on robustness of location of roots of polynomials in given regions of the complex plane for unknown but bounded perturbations on the polynomial coefficients. A geometric approach in coefficient space is exploited to derive maximal deviations (in a given class of admissible perturbations) of characteristic polynomial coefficients of an uncertain linear system from their nominal values preserving system poles in a given region of the complex plane. It is also shown that the solution of this problem can be used to give computationally feasible necessary and sufficient conditions such that all the roots of the members of a family of polynomials lie in a given open region of the complex plane. This last result can be considered an extension of the result of the well-known theorem of Kharitonov. It is also outlined how the proposed technique can be used to deal with families of polynomials with linearly correlated coefficient perturbations
Set membership localization of mobile robots via angle measurements
No full textThis paper addresses the localization problem for a mobile robot navigating in an unstructured outdoor environment. A new technique is introduced, for computing an estimate of the position of the robot and the related uncertainty region, in the presence of visual angle measurements affected by bounded errors. The proposed set membership estimation procedure exploits the structure of the static set estimator, to solve recursively the dynamic localization problem
Regularity conditions for the stability margin problem with linear dependent perturbations
No full textIn this paper, the problem of continuity of the stability margin of a control system on problem input data is addressed. The case in which perturbations are linearly correlated is considered. It is shown that the existence of special points (called critical points) in the stability boundary manifold in parameter space plays a key role in the analysis of the problem. Several conditions, either sufficient or both necessary and sufficient, are given, ensuring continuity of the stability margin on problem data. The obtained conditions turn out to be easily checkable for practical applications. Numerical examples are presented to illustrate the proposed techniques
Some results on theasymptotic stability of second order nonlinear systems
No full textThis note gives some stability results concerning second-order systems x = f(x), where f(x) contains either linear and quadratic or linear and cubic terms in x. Following a Lyapunov-like approach, a closed-form estimate for asymptotic stability regions of such systems is derived in terms of quadratic functions and then it is optimized with respect to its area. Some application examples show the good results of the proposed method, in comparison to those obtained by the classical numerica approaches. © 1984, IEEE. All rights reserved
Information based complexity and nonparametric worst-case system identification
No full textIn this paper we review recent results on nonparametric approaches to identification of linear dynamic systems, under nonprobabilistic assumptions on measurement uncertainties. Two main categories of problems are considered in the paper: H∞ and l1 settings. The H∞ setting assumes that the true system is linear time-invariant and the available information is represented by samples of the frequency response of the system, corrupted by an l∞-norm bounded noise. The aim is to estimate a proper, stable finite-dimensional model. The estimation error is quantified according to an H∞ norm, measuring the "distance" of the estimated model from the worst-case system in the class of allowable systems, for the worst-case realization of the measurement error. In the l1 setting, the aim is to identify the samples of the impulse response of an unknown linear time-invariant system. The available information is given by input/output measurements corrupted by l∞-bounded noise and the estimation error is measured according to an l1 norm, for the worst case with respect to allowable systems and noise. In this paper, the main results available in the literature for both settings are reviewed, with particular attention to (a) evaluation of the diameter of information under various experimental conditions, (b) convergence to zero of the diameter of information (i.e., existence of robustly convergent identification procedures), and (c) computation of optimal and almost-optimal algorithms. Some results are also reported for the l∞ setting, similar to the l1 setting, with the exception of the estimation error, which is measured by an l∞ norm. © 1993 by Academic Press, Inc
A new fast algorithm for robust stability analysis of linear control systems with linearly correlated parametric uncertainties
No full textIn this paper a fast algorithm is proposed for the computation of stability margins in parameter space for linear control systems subject to structured uncertainties. The case in which plant transfer function coefficients are affine in a set of physical uncertain parameters is considered. The paper shows also how the proposed algorithm can be used to solve another interesting problem in robust control analysis, i.e. the determination of the region of pole location of a closed loop control system including an entire family of uncertain plants
Visual servoing for large camera displacements
No full textThe first aim of any visual-servoing strategy is to avoid features being lost from the field of view and that the desired location may not be reached. However, avoiding both these system failures turns out to be very difficult, especially when the initial and desired locations are distant. Moreover, the methods that succeed in presence of large camera displacements often produce a long translational trajectory that may not be allowed by the robot workspace and/or joint limits. In this paper, a new strategy for dealing with such problems is proposed, which consists of generating circular-like trajectories that may satisfy the task requirements more naturally than other solutions. Knowledge of geometrical models of the object or points depth is not required. It is shown that system failures are avoided for a calibrated camera. Moreover, necessary and sufficient conditions are provided for establishing tolerable errors on the estimates of the intrinsic and extrinsic parameters, in order to guarantee a robust field of view and robust local asymptotic stability. Several simulation results show that the translational trajectories obtained in presence of large displacements are significantly shorter than those produced by the existing methods, in cases of both correct and bad camera calibration. Very satisfactory results are achieved also in presence of small displacements. © 2004 IEEE.link_to_subscribed_fulltex
Frequency response of interval plant-controller families of transfer functions
No full textIn this paper a general frequency domain result for families of interval plant with a fixed linear controller is given. It is shown that the locus of the polar diagrams of frequency responses of the transfer functions of an interval plant-controller family is bounded by the polar plots relative to the 32 segments of transfer functions of the interval plant family. Easy proofs of several important results, such as the generalization of the Theorem of Kharitonov for feedback systems with interval plants or the robust version of the small gain theorem for the same class of systems, are constructed by using the general result. More importantly, an immediate consequence of the main theorem is that extremal phase/gain margins or sensitivity/complementary sensitivity peaks for systems of the family can be deduced from those of the 32 segments of the interval plant family
Robust stability of state space models with structured uncertainties
No full textIn this paper, a method for robust eigenvalue location analysis of linear state-space models affected by structured real parametric perturbations is proposed. The approach, based on algebraic matrix properties, deals with state-space models where system matrix entries are perturbed by polynomial functions of a set of physical uncertain parameters. A method converting the robust stability problem in the nonsingularity analysis of a suitable matrix is proposed. The method leads to positivity check of a multinomial form over a hyperrectangular domain in parameter space. This problem, which can be reduced to finding the real solutions of a system of polynomial equations, simplifies considerably when considering cases with one or two uncertain parameters. For these cases, necessary and sufficient conditions for stability are given in terms of the solution of suitable real eigenvalue problems. © 1990 IEE
- …
