This paper deals with a central issue in bifurcations and chaos control applications, i.e., the stabilization of periodic motions in sinusoidally forced nonlinear systems. Specifically, the problem of designing multi-input-multi-output (MIMO) finite-dimensional linear time-invariant controllers maximizing the amplitude of the sinusoidal input for which the corresponding periodic solutions are guaranteed to be stable, is considered. By exploiting linearization techniques and the multi-variable circle criterion, a synthesis algorithm is developed to determine the controller which maximizes a suitable lower bound of the amplitude of the input. The algorithm requires the solution of a sequence of linear matrix inequalities (LMIs) of increasing size. The Brusselator oscillator is employed as a case study to show that the synthesized controllers, though optimizing a lower bound, provide quite satisfactory control performance.

Synthesis of MIMO controllers for extending the stability range of periodic solutions in forced nonlinear systems / G. BAGNI; M. BASSO; R. GENESIO; A. TESI. - In: AUTOMATICA. - ISSN 0005-1098. - STAMPA. - 41:(2005), pp. 645-654. [10.1016/j.automatica.2004.09.014]

Synthesis of MIMO controllers for extending the stability range of periodic solutions in forced nonlinear systems

BAGNI, GIANNI;BASSO, MICHELE;GENESIO, ROBERTO;TESI, ALBERTO
2005

Abstract

This paper deals with a central issue in bifurcations and chaos control applications, i.e., the stabilization of periodic motions in sinusoidally forced nonlinear systems. Specifically, the problem of designing multi-input-multi-output (MIMO) finite-dimensional linear time-invariant controllers maximizing the amplitude of the sinusoidal input for which the corresponding periodic solutions are guaranteed to be stable, is considered. By exploiting linearization techniques and the multi-variable circle criterion, a synthesis algorithm is developed to determine the controller which maximizes a suitable lower bound of the amplitude of the input. The algorithm requires the solution of a sequence of linear matrix inequalities (LMIs) of increasing size. The Brusselator oscillator is employed as a case study to show that the synthesized controllers, though optimizing a lower bound, provide quite satisfactory control performance.
2005
41
645
654
G. BAGNI; M. BASSO; R. GENESIO; A. TESI
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/224907
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