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Composite systems with uncertain couplings of fixed structure : scaled Riccati equations and the problem of quadratic stability
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Hinrichsen, Diederich and Pritchard, A. J.. (2008) Composite systems with uncertain couplings of fixed structure : scaled Riccati equations and the problem of quadratic stability. SIAM Journal on Control and Optimization, Volume 47 (Number 6). pp. 30373075. ISSN 03630129
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Official URL: http://dx.doi.org/10.1137/070707919
Abstract
We consider large scale systems consisting of a finite number of separate uncertain subsystems which interact via uncertain couplings of arbitrarily prescribed structure. The couplings are viewed as structured perturbations of the blockdiagonal system representing the collection of the separate nominal subsystems (the "nominal system"). We de. ne spectral value sets and stability radii for these timeinvariant structured perturbations and derive formulas for their computation. Scaled Riccati equations are introduced to obtain explicit formulas for the stability radii with respect to timevarying and possibly nonlinear perturbations of the given structure. From these we derive necessary and sufficient conditions under which the stability radii with respect to timeinvariant and timevarying perturbations are equal. These results are obtained by constructing joint quadratic Liapunov functions of optimal robustness. With their help we prove necessary and sufficient conditions for quadratic stability and sufficient conditions for the validity of a generalized Aizerman conjecture.
Item Type:  Journal Article  

Subjects:  Q Science > QA Mathematics  
Divisions:  Faculty of Science > Mathematics  
Library of Congress Subject Headings (LCSH):  Riccati equation, Perturbation (Mathematics), System theory, Spectral theory (Mathematics), Stability, Nonlinear control theory  
Journal or Publication Title:  SIAM Journal on Control and Optimization  
Publisher:  Society for Industrial and Applied Mathematics  
ISSN:  03630129  
Official Date:  2008  
Dates: 


Volume:  Volume 47  
Number:  Number 6  
Number of Pages:  39  
Page Range:  pp. 30373075  
Identification Number:  10.1137/070707919  
Status:  Peer Reviewed  
Publication Status:  Published  
Access rights to Published version:  Restricted or Subscription Access  
References:  [1] F. Amato, Robust Control of Linear Systems Subject to Uncertain TimeVarying Perturbations, 

URI:  http://wrap.warwick.ac.uk/id/eprint/28555 
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