A homotopy LMI approach to design robust H/sub 2/ controller for Lur´e systems with multiple slope restrictions

This paper presents a novel approach of the robust H/sub 2/ controller design for linear time-invariant systems subject to real parametric uncertainty. The uncertainty set is described by memoryless, time-invariant, sectorbounded, and slope-restricted nonlinearities. The controller synthesis is formulated as nonlinear optimization over bilinear matrix inequalities. By eliminating the dynamic matrix of design variables and alternating between three different linear matrix inequality problems, locally optimal solutions can be obtained. The numerical examples show that our designed robust controllers can retain stability and improve performance of the closed-loop uncertain systems. Therefore, the unified approach leads to an effective design tool which guarantees both stability and performance of linear time-invariant systems under real parametric uncertainty.