Pole-assignment robustness in a specified disk

doi:10.1016/0167-6911(91)90027-C

Systems & Control Letters

Volume 16, Issue 1, January 1991, Pages 41-44

https://doi.org/10.1016/0167-6911(91)90027-C Get rights and content

Abstract

A sufficient condition is proposed to guarantee robust pole location within a specified circular region for a linear uncertain system. The explicit bounds on linear time-invariant perturbations with highly structured information are obtained. Under these allowable highly structured perturbations, both stability robustness and certain performance robustness will thus be ensured. The merit of the proposed new approach is demonstrated by a given example where the results achieved are much better than the ones reported recently.

References (8)

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Pole assignment in a specified disk
IEEE Trans. Automat. Control
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N. Kawasaki et al.
Pole placement in a specified region based on a linear quadratic regulator
Internat. J. Control.
(1988)

There are more references available in the full text version of this article.

Cited by (76)

Robust pole assignment in a specified union region using harmony search algorithm
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In these cases, the applicable scopes are limited for the proposed methods. Another approach considers region robust pole assignment and it focuses on placing the desired poles in a pre-specified region of the complex plane and ensuring the poles of the closed-loop system remain within the specified region when the system perturbation or uncertainty appears (see e.g., [32–49]). A method for pole assignment in a specified disk for linear feedback control systems based on the Riccati equation with norm-bounded uncertainty was studied in [33,39].
This paper considers the problem of robust pole assignment for linear time-invariant systems by state feedback in a single circular region or a set of disjoint circular regions. A sufficient condition for the robust measure object is derived and it ensures the poles of the closed-loop system to remain within the specified union region when the perturbation or uncertainty appears. In order to get a set of poles and the corresponding state feedback controller which allow the system to have a maximum allowable perturbation or uncertainty for region pole constraint, the harmony search algorithm is employed to address the related optimization problem based on stochastic optimization approach. The simulation results demonstrate the effectiveness of the proposed approach.
Robust pole-clustering of structured uncertain systems in union of disjointed circular regions
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The robustness properties of uncertain systems are commonly investigated using matrix analysis techniques. For example, Chou [12] and Gardiner [13] derived the robustness conditions of systems with structured uncertainties using the spectral radius of the system matrix. Zhou and Khargonekar [30] discussed the stability robustness bound using the properties of maximum singular value.
This paper presents a systematic procedure for depicting the robust pole-clustering of a system with structured uncertainties. Different from many previous researches on connected region, a union of disjointed circular regions on the complex plane containing either a single-nominal pole or multi-nominal poles is obtained utilizing matrix operation. In addition, a criterion for determining the allowable perturbation bounds of the structured uncertain system such that the pole clusters remain within certain pre-specified circular regions is also proposed. The validity of the proposed approach is confirmed by way of numerical examples.
Robust eigenvalue-clustering in a specified circular region for linear uncertain discrete singular systems with state delay
2007, Applied Mathematics and Computation
In this paper, the robust eigenvalue-clustering in a specified circular region problem (i.e., the robust D-stability problem) of linear discrete singular time-delay systems with structured (elemental) parameter uncertainties is investigated. Under the assumptions that the linear nominal discrete singular time-delay system is regular and causal, and has all its finite eigenvalues lying inside a specified circular region, a new sufficient condition is proposed to preserve the assumed properties when the structured parameter uncertainties are added into the linear nominal discrete singular time-delay system. When all the finite eigenvalues are just required to locate inside the unit circle of the z-plane, the proposed criterion will become the stability robustness criterion. The presented criterion is mathematically proved to be less conservative than the existing ones reported very recently in the literature.
Robust D-stability analysis for linear uncertain discrete singular systems with state delay
2006, Applied Mathematics Letters
In this work, by using the maximum modulus principle and the spectral radii of matrices, a new robust D-stability (i.e., robust eigenvalue clustering in a specified circular region) condition is proposed to ensure that, for all admissible structured parameter uncertainties, the linear discrete singular system with state delay is regular, causal and D-stable. The proposed criterion is mathematically proved to be less conservative than the existing one reported very recently.
Another sufficient condition for the stability of grey discrete-time systems
2005, Journal of the Franklin Institute
In this paper, the stability of grey discrete-time systems is discussed whose state matrices are interval matrices. A new approach is obtained which guarantee the stability of grey discrete-time systems. The sufficient condition for robust stability of grey time delay systems subjected to interval systems is also derived. By mathematical analysis, the stability criterion is less conservative than those in previous results. Examples are given to compare the proposed method with reported recently.
Output feedback pole-placement in damping region for discrete-time uncertain polytopic systems
2024, International Journal of Systems Science

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Pole-assignment robustness in a specified disk

Abstract

Linear System Theory and Design

Robust Analysis and Design of Multiloop Control Systems

Pole assignment in a specified disk

IEEE Trans. Automat. Control

Pole placement in a specified region based on a linear quadratic regulator

Internat. J. Control.