Pseudospectral Components and the Distance to Uncontrollability
نویسندگان
چکیده
We show that 2-norm pseudospectra ofm-by-nmatrices have no more than 2m(4m−1) connected components. Such bounds are pertinent for computing the distance to uncontrollability of a control system, since this distance is the minimum value of a function whose level sets are pseudospectra. We also discuss algorithms for computing this distance, including a trisection variant of Gu’s recent algorithm, and we show how these may be used to locally maximize the distance to uncontrollability for a parameterized system.
منابع مشابه
Measures for Robust Stability and Controllability
A linear time-invariant dynamical system is robustly stable if the system and all of its nearby systems in a neighborhood of interest are stable. An important property of robustly stable systems is that they decay asymptotically without exhibiting significant transient behavior. The first part of this thesis work focuses on measures revealing the degree of robust stability. We put special empha...
متن کاملOn the structured distance to uncontrollability
This article is concerned with the structured distance to uncontrollability of a linear time-invariant system and relates this concept to a variation of the μ-value. The developed framework is applied to derive computational expressions for the class of real perturbations as well as for Hermitian, symmetric, and skew-symmetric perturbations in a relatively simple manner. Examples demonstrate th...
متن کاملرابطه باورهای فراشناختی با اختلال افسردگی و اضطراب
Background : Metacognitive beliefs interact with emotional disorders and this matter can be used in educational programs and psychological interventions. The purpose of this study was to investigate the relationship between metacognitive beliefs and anxiety and depression. Materials and Methods: In this correlation study, at first, 140 persons were chosen with cluster sampling method. They com...
متن کاملFast Methods for Estimating the Distance to Uncontrollability
The distance to uncontrollability for a linear control system is the distance (in the 2-norm) to the nearest uncontrollable system. We present an algorithm based on methods of Gu and Burke–Lewis–Overton that estimates the distance to uncontrollability to any prescribed accuracy. The new method requires O(n4) operations on average, which is an improvement over previous methods which have complex...
متن کاملThe structured distance to uncontrollability under multi-perturbations: An approach using multi-valued linear operators
In this paper we develop a unifying approach for computing the distance to uncontrollability of linear control systems. By using multi-valued linear operators in representing and estimating the system's equations and matrices we are able to derive computable formulas of the distance from a controllable linear system to the nearest uncontrollable system under the assumption that the system's mat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- SIAM J. Matrix Analysis Applications
دوره 26 شماره
صفحات -
تاریخ انتشار 2004