On the global practical stabilization of discrete-time switched affine systems: Application to switching power converters

Document Type : Article


Department of Electrical Engineering, Sahand University of Technology, Sahand New Town, Tabriz, P.O. Box 51335-1996, Iran


This paper presents new sufficient conditions as a set of Bilinear
Matrix Inequalities (BMIs) for the global practical stabilization of
discrete-time switched affine systems. The main contribution is on
proposing the stability conditions based on a common quadratic
Lyapunov function that can be used to stabilize the discrete-time
switched affine systems around a desired equilibrium point for which
it is not required to find any Schur stable convex combination of
operating modes as a pre-processing stage, that needs special
algorithms and is an NP-hard problem. The result is that the
existing two-stage stabilization methods based on a pre-calculation
of a Schur stable convex combination of operating modes are
simplified to a single-stage method by which a high degree of
applicability is obtained. The proposed stability conditions are
developed in a way the size of the convergence ellipsoid is
minimized. Moreover, it is not required the equilibrium point,
around which the invariant set of attraction is constructed, be
inside a predetermined set of attainable equilibrium points. The
satisfactory operation of the proposed stability conditions is
illustrated by an academic example and application on
various DC-DC converters.


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