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

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). observer gain freely chosen and the LMIs conditions such that equivalent to control by interconnection input strictly passive (ISP) and/or output (OSP) zero detectable (ZSD) are established. It shown proposed exponentially stabilizes a class infinite-dimensional PHS asymptotically finite-dimensional non-linear PHS. A Timoshenko beam model microelectromechanical system used illustrate approach.