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See detailGlobal asymptotic stability of the limit cycle in piecewise linear versions of the Goodwin oscillator
Salinas Varela, A. A.; Stan, G. B. V.; Goncalves, Jorge UL

in Proceedings of the 17th IFAC World Congress (2008)

Conditions in the form of linear matrix inequalities (LMIs) are used in this paper to guarantee the global asymptotic stability of a limit cycle oscillation for a class of piecewise linear (PWL) systems ... [more ▼]

Conditions in the form of linear matrix inequalities (LMIs) are used in this paper to guarantee the global asymptotic stability of a limit cycle oscillation for a class of piecewise linear (PWL) systems defined as the feedback interconnection of a saturation controller with a single input, single output (SISO) linear time-invariant (LTI) system. The proposed methodology extends previous results on impact maps and surface Lyapunov functions to the case when the sets of expected switching times are arbitrarily large. The results are illustrated on a PWL version of the Goodwin oscillator. [less ▲]

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