Passivity analysis of rational LPV systems using Finsler’s lemma

Polcz, Péter and Kulcsár, Balázs and Péni, Tamás and Szederkényi, Gábor (2019) Passivity analysis of rational LPV systems using Finsler’s lemma. In: Conference on Decision and Control, 2019 dec. 11-13, Nice, France.

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Abstract

In this paper, we show and utilize new results on the relationship between passivity, zero dynamics and stable dynamic invertibility of linear parameter-varying (LPV) sys- tems. Furthermore, an optimization-based systematic passivity analysis procedure and a passivating output projection are proposed for asymptotically stable rational LPV systems in the linear fractional representation (LFR) form having at least as many independent output signals as input signals. The storage function is searched in a quadratic form with a symmetric rational parameter-dependent matrix. In order to form a square system and then to satisfy the Kalman-Yakubovich- Popov (KYP) properties, a parameter-dependent output pro- jection matrix is searched in the LFR form. The nonlinear parameter dependence from the linear matrix inequality (LMI) and equality (LME) conditions provided by the KYP lemma is factorized out using the linear fractional transformation (LFT). Then, Finsler’s lemma and affine annihilators are used to relax the sufficient affine parameter-dependent LMI and LME conditions. As an application example, a stable system inversion is addressed and demonstrated on a benchmark rational LPV model.

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