Absolute stabilization of Lur'e systems via dynamic output feedback

In this paper, we study the problem of absolute stabilization under dynamic output feedback for Lur'e systems with sector-bounded unknown nonlinearities. In most of the literature, besides the incremental sector-boundedness condition, the Lur'e-type nonlinearity itself is assumed to be known exactly and used in the dynamic output feedback controller design. In the present paper only the sector-boundedness condition is employed, and exact knowledge of the nonlinearity will not be used in the controller design. More precisely, we will only employ knowledge of the sector in which the unknown nonlinearity lies. Two different approaches will be presented for the dynamic controller design, both using linear matrix inequality techniques. Numerical simulations of a flexible joint robotic arm will illustrate the theoretical results obtained in this paper.