Reference
M. Hajiahmadi, B. De Schutter, and H. Hellendoorn, "Stabilization and robust
H
∞ control for sector-bounded switched nonlinear systems,"
Automatica, vol. 50, no. 10, pp. 2726-2731, Oct. 2014.
Abstract
This paper presents stability analysis and robust H
∞ control
for a particular class of switched systems characterized by nonlinear functions
that belong to sector sets with arbitrary boundaries. The sector boundaries can
have positive and/or negative slopes, and therefore, we cover the most general
case in our approach. Using the special structure of the system but without
making additional assumptions (e.g. on the derivative of the nonlinear
functions), and by proposing new multiple Lyapunov function candidates, we
formulate stability conditions and a control design procedure in the form of
matrix inequalities. The proposed Lyapunov functions are more general than the
quadratic functions previously proposed in the literature, as they incorporate
the nonlinearities of the system and hence, lead to less conservative stability
conditions. The stabilizing switching controllers are designed through a
bi-level optimization problem that can be efficiently solved using a
combination of a convex optimization algorithm and a line search method. The
proposed optimization problem is achieved using a special loop transformation
to normalize the arbitrary sector bounds and by other linear matrix
inequalities (LMI) techniques.
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BibTeX
@article{HajDeS:14-022,
author = {Hajiahmadi, Mohammad and De Schutter, Bart and Hellendoorn,
Hans},
title = {Stabilization and Robust ${H}_{\infty}$ Control for
Sector-Bounded Switched Nonlinear Systems},
journal = {Automatica},
volume = {50},
number = {10},
pages = {2726--2731},
month = oct,
year = {2014}
}