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Real and Complex Stability Radii of Polynomial Matrices
"... In this paper, analytic expressions are derived for the complex and real stability radii of nonmonic polynomial matrices with respect to an arbitrary stability region of the complex plane. Numerical issues for computing these radii for di#erent perturbation structures are also considered with appli ..."
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In this paper, analytic expressions are derived for the complex and real stability radii of nonmonic polynomial matrices with respect to an arbitrary stability region of the complex plane. Numerical issues for computing these radii for di#erent perturbation structures are also considered with application to robust stability of Hurwitz and Schur polynomial matrices. 1
Robustness Analysis for Systems with Ellipsoidal Uncertainty
 International Journal of Robust and Nonlinear Control
, 1998
"... Introduction The generalized structured singular value (¯) introduced by Chen, Fan, and Nett [3, 4] unified and extended the wellknown Kharitonovlike stability conditions. The Kharitonovlike stability conditions correspond to a generalized ¯ problem of rank one, which can be written as a convex o ..."
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Introduction The generalized structured singular value (¯) introduced by Chen, Fan, and Nett [3, 4] unified and extended the wellknown Kharitonovlike stability conditions. The Kharitonovlike stability conditions correspond to a generalized ¯ problem of rank one, which can be written as a convex optimization problem that is readily computable, often as an explicit analytical expression. These simple computations are in sharp contrast to the general robustness margin computation problem, which is NPhard [2]. As an application of their main result [3], Chen et al derived explicit conditions for the robustness margins of interval and diamond polynomials whose coefficients are perturbed in an affine fashion [4]. However, ellipsoidal uncertainty descriptions are more naturally obtained from parameter identification procedures [7]. Previouslyderived conditions for computing robustness margins for systems with ellipsoidal uncertainties apply only to
273 Calculation of stability margins and design of robust controllers for multilinear systems
, 2000
"... Consider a linear timeinvariant system with uncertain parameters. One can study the performance of the uncertain system by investigating the effects of uncertainties on the characteristic equation of the system. Different methods have already been presented for the calculation of the bounds of allo ..."
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Consider a linear timeinvariant system with uncertain parameters. One can study the performance of the uncertain system by investigating the effects of uncertainties on the characteristic equation of the system. Different methods have already been presented for the calculation of the bounds of allowable parameter variations and the design of robust controllers for such systems. In a few recent papers ([1], [2]), the Minimum Distance Function (MDF) method is developed to address the above problems. The cases where the coefficients of the characteristic polynomials are linearly dependent on uncertain parameters, have already been investigated. In this paper, the more general and the more realistic case of polynomials with multilinearlydependent coefficients is investigated. The MDF method is generalised to this case and a new algorithm for the calculation of allowable parameter perturbations is presented. The algorithm requires the numerical solution of a system of equations in each fr...
The Rank One Mixed µ Problem and "KharitonovType" Analysis
 Manuscript in Preparation
"... The general mixed problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed problem. We show ..."
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The general mixed problem has been shown to be NP hard, so that the exact solution of the general problem is computationally intractable, except for small problems. In this paper we consider not the general problem, but a particular special case of this problem, the rank one mixed problem. We show that for this case the mixed problem is equivalent to its upper bound (which is convex), and it can in fact be computed easily (and exactly). This special case is shown to be equivalent to the so called "affine parameter variation" problem (for a polynomial with perturbed coefficients) which has been examined in detail in the literature, and for which several celebrated "Kharitonovtype" results have been proven. 1 Introduction It is now known that the general mixed problem is NP hard, and this strongly suggests that the exact solution of the general problem is computationally intractable, except for small problems [3]. In this paper we consider not the general problem, but a particular ...
Stability Bounds for Higher Order Linear Dynamical Systems
 in Fourteenth International Symposium of Mathematical Theory of Networks and Systems
, 2000
"... This paper derives analytic expressions for the real stability radius of polynomial matrices with respect to an arbitrary region in the complex plane. We are also discussing numerical issues for computing these radii for different perturbation structures, with application to robust stability of Hurw ..."
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This paper derives analytic expressions for the real stability radius of polynomial matrices with respect to an arbitrary region in the complex plane. We are also discussing numerical issues for computing these radii for different perturbation structures, with application to robust stability of Hurwitz and Schur polynomial matrices. 1
Formally reviewed communication A note on a nearest polynomial with a given root
"... In this paper, we consider the problem of a nearest polynomial with a given root in the complex field (the coefficients of the polynomial and the root are complex numbers). We are interested in the existence and the uniqueness of such polynomials. Then we study the problem in the real case (the coef ..."
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In this paper, we consider the problem of a nearest polynomial with a given root in the complex field (the coefficients of the polynomial and the root are complex numbers). We are interested in the existence and the uniqueness of such polynomials. Then we study the problem in the real case (the coefficients of the polynomial and the root are real numbers), and in the realcomplex case (the coefficients of the polynomial are real numbers and the root is a complex number). We derive new formulas for computing such polynomials.