Robust D-Stabilisation of Uncertain Systems via Static Output Feedback

In this paper, a robust static output feedback (SOF) D-stabilisation design strategy for uncertain linear time-invariant (LTI) systems is proposed. The SOF controller design is based on a two-stage method and the robust static gains are obtained by solving a set of linear matrix inequalities (LMI) conditions. The D-region considered for the eigenvalue placement is a circle in the complex left half-plane which is defined according to two scalar parameters. We also propose more relaxed conditions for the SOF controller design, when compared to the conservative preliminary LMI constraints, by considering parameter-dependent Lyapunov functions (PDLF) and parameter-dependent Finsler's Lemma additional variables (PDFV). Some academic examples are presented in order to attest for the validity of the proposed results, followed by a practical implementation on an active suspension system, assuming that the feedback loop is composed by only one of its four system state variables.