Explicit formulae for stability radii of positive polynomial matrices
نویسندگان
چکیده
In this paper we study stability radii of positive polynomial matrices under affine perturbations of the coefficient matrices. It is shown that the real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by some examples.
منابع مشابه
Stability radii of higher order positive difference systems
In this paper we study stability radii of positive polynomial matrices under a2ne perturbations of the coe2cient matrices. 9 It is shown that the real and complex stability radii coincide. Moreover, explicit formulas are derived for these stability radii and illustrated by some examples. 11 c © 2003 Published by Elsevier Science B.V.
متن کاملReal and complex stability radii of polynomial matrices
In this paper, analytic expressions are derived for the complex and real stability radii of non-monic polynomial matrices with respect to an arbitrary stability region of the complex plane. Numerical issues for computing these radii for different perturbation structures are also considered with application to robust stability of Hurwitz and Schur polynomial matrices.
متن کاملRecurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials
Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$ x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x),$$ we find the coefficients $b_{i,j}^{(p,q,ell ,,r)}$ in the expansion $$ x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell }y^{r}f^{(p,q)}(x,y) =sumli...
متن کاملGershgorin-Brualdi Perturbations and Riccati Equations
For uncertain linear systems with complex parameter perturbations of static output feedback type a quadratic Liapunov function of maximal robustness was constructed in [5]. Such Liapunov functions can be used to ensure the stability of uncertain systems under arbitrary nonlinear and time-varying perturbations which are smaller than the stability radius. In this paper we establish analogous resu...
متن کاملExplicit polar decomposition of complex matrices
In [F. Uhlig, Explicit polar decomposition and a near-characteristic polynomial: The 2 × 2 case, Linear Algebra Appl., 38:239–249, 1981], the author gives a representation for the factors of the polar decomposition of a nonsingular real square matrix of order 2. Uhlig’s formulae are generalized to encompass all nonzero complex matrices of order 2 as well as all order n complex matrices with ran...
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:
دوره شماره
صفحات -
تاریخ انتشار 2002