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Hybrid dynamical systems can exhibit many unique phenomena, such as Zeno behavior. Zeno behavior is the occurrence of infinite discrete transitions in finite time. Zeno behavior has been likened to a form of finitetime asymptotic stability, and corresponding Lyapunov theorems have been developed. In this paper, we propose a method to construct Lyapunov functions to prove Zeno stability of compact sets in cyclic hybrid systems with parametric uncertainties in the vector fields, domains and guard sets, and reset maps utilizing sum-ofsquares programming. This technique can easily be applied to cyclic hybrid systems without parametric uncertainties as well. Examples illustrating the use of the proposed technique are also provided.

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

Hejri

2020

Scientia Iranica

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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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Cited by 3 publications

References 107 publications

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A sum-of-squares approach to the analysis of Zeno stability in polynomial hybrid systems

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

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