Linear Matrix Inequality Design of Exponentially Stabilizing Observer-Based State Feedback Port-Hamiltonian Controllers

Jesus Toledo (1) , H. Ramirez (2) , Y. Wu (3) , Y. Le Gorrec (3)

1 DTIS, ONERA, Université de Toulouse [Toulouse]
2 UTFSM - Universidad Tecnica Federico Santa Maria [Valparaiso]
3 FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174)

The design of an observer-based state feedback (OBSF) controller with guaranteed passivity properties for port-Hamiltonian systems (PHS) is addressed using linear matrix inequalities (LMIs). The observer gain is freely chosen and the LMIs conditions such that the state feedback is equivalent to control by interconnection with an input strictly passive (ISP) and/or an output strictly passive (OSP) and zero state detectable (ZSD) port-Hamiltonian controller are established. It is shown that the proposed controller exponentially stabilizes a class of infinite-dimensional PHS and asymptotically stabilizes a class of finite-dimensional non-linear PHS. A Timoshenko beam model and a microelectromechanical system are used to illustrate the proposed approach.

Mots clés: Port-Hamiltonian systems; boundary control systems; nonlinear systems; state feedback; Luenberger observer; linear matrix inequality

Domaines: Automatique / Robotique

Jesus Toledo, H. Ramirez, Y. Wu, Y. Le Gorrec. Linear Matrix Inequality Design of Exponentially Stabilizing Observer-Based State Feedback Port-Hamiltonian Controllers. IEEE Transactions on Automatic Control, In press, ⟨10.1109/TAC.2022.3227927⟩. ⟨hal-04105140⟩