The problem of the estimation of the domain of attraction for Impulsive Dynamical Systems (IDSs) is tackled in this paper. IDSs are a special class of hybrid systems that exhibit jumps in the state trajectory, which can be either time-driven (time-dependent IDSs), or driven by specific state values (state-dependent IDSs). Sufficient conditions to determine whether a polytope belongs to the domain of attraction of the zero equilibrium point are provided for both time-dependent and state-dependent IDS, when a nonlinear quadratic continuous-time dynamic is considered. The proposed results are stated in terms of Linear Matrix Inequalities problems. The effectiveness of the proposed results is shown by means of the analysis of a biological model for tumor progression. (C) 2010 Elsevier Ltd. All rights reserved.

Estimation of the domain of attraction for a class of hybrid systems

AMBROSINO, ROBERTO;
2011

Abstract

The problem of the estimation of the domain of attraction for Impulsive Dynamical Systems (IDSs) is tackled in this paper. IDSs are a special class of hybrid systems that exhibit jumps in the state trajectory, which can be either time-driven (time-dependent IDSs), or driven by specific state values (state-dependent IDSs). Sufficient conditions to determine whether a polytope belongs to the domain of attraction of the zero equilibrium point are provided for both time-dependent and state-dependent IDS, when a nonlinear quadratic continuous-time dynamic is considered. The proposed results are stated in terms of Linear Matrix Inequalities problems. The effectiveness of the proposed results is shown by means of the analysis of a biological model for tumor progression. (C) 2010 Elsevier Ltd. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11367/19465
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