A local field of extremals for single-input systems with state space constraints

2004 ◽  
Author(s):  
U. Ledzewicz ◽  
H. Schattler
Keyword(s):  
State Space ◽  
Local Field ◽  
Single Input ◽  
Field Of Extremals

scholarly journals Extracting second-order structures from single-input state-space models: Application to model order reduction

2011 ◽  
Vol 21 (3) ◽  
pp. 509-519 ◽  
Author(s):  
Jérôme Guillet ◽  
Benjamin Mourllion ◽  
Abderazik Birouche ◽  
Michel Basset
Keyword(s):  
State Space ◽  
Model Order Reduction ◽  
Order Reduction ◽  
Second Order ◽  
Input State ◽  
Model Order ◽  
New Approach ◽  
Order Form ◽  
Form Model ◽  
Single Input

Extracting second-order structures from single-input state-space models: Application to model order reductionThis paper focuses on the model order reduction problem of second-order form models. The aim is to provide a reduction procedure which guarantees the preservation of the physical structural conditions of second-order form models. To solve this problem, a new approach has been developed to transform a second-order form model from a state-space realization which ensures the preservation of the structural conditions. This new approach is designed for controllable single-input state-space realizations with real matrices and has been applied to reduce a single-input second-order form model by balanced truncation and modal truncation.

scholarly journals Equivalence of Control Systems on the Pseudo-Orthogonal Group SO (2, 1)0

2016 ◽  
Vol 24 (2) ◽  
pp. 45-65 ◽  
Author(s):  
Rory Biggs ◽  
Claudiu C. Remsing
Keyword(s):  
State Space ◽  
Control Systems ◽  
Equivalence Class ◽  
Lie Group ◽  
Orthogonal Group ◽  
Full Rank ◽  
Input Control ◽  
The Matrix ◽  
Single Input ◽  
Invariant Control

AbstractWe consider left-invariant control affine systems on the matrix Lie group SO (2, 1)0. A classification, under state space equivalence, of all such full-rank control systems is obtained. First, we identify certain subsets on which the group of Lie algebra automorphisms act transitively. We then systematically identify equivalence class representatives (for single-input, two-input and three-input control systems). A brief comparison of these classification results with existing results concludes the paper.

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