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  1. Annali di Matematica Pura ed Applicata
  2. Annali di Matematica Pura ed Applicata : Volume 176
  3. Annali di Matematica Pura ed Applicata : Volume 176, Issue 1, December 1999
  4. On the definiteness of quadratic functionals
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Annali di Matematica Pura ed Applicata : Volume 196
Annali di Matematica Pura ed Applicata : Volume 195
Annali di Matematica Pura ed Applicata : Volume 194
Annali di Matematica Pura ed Applicata : Volume 193
Annali di Matematica Pura ed Applicata : Volume 192
Annali di Matematica Pura ed Applicata : Volume 191
Annali di Matematica Pura ed Applicata : Volume 190
Annali di Matematica Pura ed Applicata : Volume 189
Annali di Matematica Pura ed Applicata : Volume 188
Annali di Matematica Pura ed Applicata : Volume 187
Annali di Matematica Pura ed Applicata : Volume 186
Annali di Matematica Pura ed Applicata : Volume 185
Annali di Matematica Pura ed Applicata : Volume 184
Annali di Matematica Pura ed Applicata : Volume 183
Annali di Matematica Pura ed Applicata : Volume 182
Annali di Matematica Pura ed Applicata : Volume 181
Annali di Matematica Pura ed Applicata : Volume 180
Annali di Matematica Pura ed Applicata : Volume 179
Annali di Matematica Pura ed Applicata : Volume 178
Annali di Matematica Pura ed Applicata : Volume 177
Annali di Matematica Pura ed Applicata : Volume 176
Annali di Matematica Pura ed Applicata : Volume 176, Issue 1, December 1999
The wave equation on homogeneous trees
Minimizing movements and evolution problems in Euclidean spaces
Metrizable extensions of dynamical systems from function algebras
Global random attractors are uniquely determined by attracting deterministic compact sets
Hyperbolicity outside a compact set and homogeneous spaces
Géodésiques complexes et rétractes holomorphes de dimension 1
On some geometrical problems of paperfolding
On the definiteness of quadratic functionals
Families of Liapunov-Krasovskiį functionals and stability for functional differential equations
Evolution equations associated with non-isothermal phase separation: Subdifferential approach
Chaos in singular systems
On pointwise multipliers forF p, q s (ℝn) in caseσ p, q
Abelian integrals for cubic vector fields
Regularity of the solution and of the free boundary for free boundary problems arising in combustion theory
Leray residues and Abel's theorem inCR codimensionk
Homoclinics and chaotic behaviour for perturbed second order systems
On an infinite interval boundary value problem
Annali di Matematica Pura ed Applicata : Volume 175
Annali di Matematica Pura ed Applicata : Volume 174
Annali di Matematica Pura ed Applicata : Volume 173
Annali di Matematica Pura ed Applicata : Volume 172

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On the definiteness of quadratic functionals

Content Provider Springer Nature Link
Author Kratz, Werner Liebscher, Dirk Schätzle, Reiner
Copyright Year 1999
Abstract In this paper we derive various characterizations of strong observability (or observability with unknown inputs) of time-dependent linear systems $$\dot x = Ax + Bu,y = C_0 x$$ with state x, control u, and output y, provided that the matrices A, B, and C0 are smooth enough. We show that strong observability is equivalent to the definiteness of a corresponding quadratic functional, and particularly to a certain asymptotic behaviour of solutions of associated Riccati matrix differential equations. The main tools for the proofs are an application of Ehrling's lemma and a characterization of strong observability via a rank condition on matrices, which are built up from derivatives of the matrices A, B, and C0.
Starting Page 133
Ending Page 143
Page Count 11
File Format PDF
ISSN 03733114
Journal Annali di Matematica Pura ed Applicata
Volume Number 176
Issue Number 1
e-ISSN 16181891
Language English
Publisher Springer-Verlag
Publisher Date 1999-01-01
Publisher Place Berlin, Heidelberg
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mathematics
Content Type Text
Resource Type Article
Subject Applied Mathematics
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