Stability Analysis of Time-Varying Systems with Harmonic Oscillations Using IQC Frequency Domain Multipliers

Jorge Ayala-Cuevas (1) , Fabricio Saggin (1) , Anton Korniienko (1) , Gérard Scorletti (1)

1 MIS - Ampère, Département Méthodes pour l'Ingénierie des Systèmes

This paper considers stability analysis of uncertain and time-varying systems containing harmonic oscillations of the form cosine and sine simultaneously. The analysis is performed by investigating the stability of a feedback interconnection through Integral Quadratic Constraints (IQC) approach. A new class of IQC multipliers, derived in frequency domain, is proposed to deal with simultaneous cosine and sine harmonic oscillations. The proposed multiplier reduces the conservatism with respect to other multipliers by exploiting frequency and phase shift information. A multiplier parameterization admitting real state-space realization is proposed. Such a parameterization allows to perform stability analysis through a finite-dimensional LMI optimization problem with a reduced number of decision variables.

Mots clés: uncertain systems; cosine harmonic oscillations; multiplier parameterization; phase shift information; sine harmonic oscillations; IQC multipliers; integral quadratic constraints approach; IQC frequency domain multipliers; time-varying systems; stability analysis

Domaines: Automatique / Robotique

Jorge Ayala-Cuevas, Fabricio Saggin, Anton Korniienko, Gérard Scorletti. Stability Analysis of Time-Varying Systems with Harmonic Oscillations Using IQC Frequency Domain Multipliers. CDC, Dec 2019, Nice, France. pp.5193-5198, ⟨10.1109/CDC40024.2019.9029738⟩. ⟨hal-03093309⟩