Convex invertible cones and the Lyapunov equation
نویسندگان
چکیده
منابع مشابه
Convex Invertible Cones, Nevalinna-Pick Interpolation and the Set of Lyapunov Solutions
For a real matrix A whose spectrum avoids the imaginary axis, it is shown that the three following, seemingly independent problems, are in fact equivalent. • Characterizing the set of real symmetric solutions of the algebraic Lyapunov inclusion associated with A. • The image of all Nevalinna-Pick interpolations associated with the spectrum of A. • The structure of the Convex Invertible Cone gen...
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If the solution of a Lyapunov or Riccati equation corresponding to a finite-dimensional system is invertible, then this leads to additional properties of this system. For infinite-dimensional systems these results do not need to hold. We show that it is necessary to put some additional conditions on the spectrum of the system operator A. For instance, if this operator has compact resolvent, the...
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In this paper, we investigate the structure of several convex cones that arise in the study of Lyapunov functions. In particular, we consider cones associated with quadratic Lyapunov functions for both linear and non-linear systems, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, we present som...
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In this paper, the structure of several convex cones that arise in the study of Lyapunov functions is investigated. In particular, the cones associated with quadratic Lyapunov functions for both linear and non-linear systems are considered, as well as cones that arise in connection with diagonal and linear copositive Lyapunov functions for positive linear systems. In each of these cases, some t...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1997
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00424-6