Passivity of nonlinear incremental systems: Application to PI stabilization of nonlinear RLC circuits

It is well known that if the linear time invariant system x ˙ = A x + B u , y = C x is passive the associated incremental system x ˜ ˙ = A x ˜ + B u ˜ , y ˜ = C x ˜ , with ( · ) ˜ = ( · ) - ( · ) ⋆ , u ⋆ , y ⋆ the constant input and output associated to an equilibrium state x ⋆ , is also passive. In...

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Bibliographic Details
Published in:Systems & control letters 2007-09, Vol.56 (9), p.618-622
Main Authors: Jayawardhana, Bayu, Ortega, Romeo, García-Canseco, Eloísa, Castaños, Fernando
Format: Article
Language:English
Subjects:
Applied sciences
Automatic
Computer science
control theory
systems
Control theory. Systems
Engineering Sciences
Exact sciences and technology
Incremental models
Nonlinear systems
Passivity
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Summary:It is well known that if the linear time invariant system x ˙ = A x + B u , y = C x is passive the associated incremental system x ˜ ˙ = A x ˜ + B u ˜ , y ˜ = C x ˜ , with ( · ) ˜ = ( · ) - ( · ) ⋆ , u ⋆ , y ⋆ the constant input and output associated to an equilibrium state x ⋆ , is also passive. In this paper, we identify a class of nonlinear passive systems of the form x ˙ = f ( x ) + gu , y = h ( x ) whose incremental model is also passive. Using this result we then prove that a large class of nonlinear RLC circuits with strictly convex electric and magnetic energy functions and passive resistors with monotonic characteristic functions are globally stabilizable with linear PI control.
ISSN:0167-6911
1872-7956
DOI:10.1016/j.sysconle.2007.03.011