Continuous-time observer-based gain-scheduled output feedback controller design with simultaneous optimization of scaling matrices

This paper addresses the design problem of continuous-time Gain-Scheduled (GS) controllers comprising GS observers and GS state-feedback controllers for continuous-time Linear Parameter-Varying (LPV) systems. In most of GS controller design for practical systems, several uncertainty blocks are introduced to represent various control requirements, similarly to scaled controller design. Then, the design problem of GS output feedback controllers is formulated in terms of a non-convex problem due to the simultaneous design of the scaling matrices for the multiple uncertainty blocks. For this practical design problem, we propose a design method in which GS observer and GS state-feedback gains as well as constant scaling matrices are simultaneously optimized by using dilated Linear Matrix Inequality (LMI) technique with some structural constraints for the matrices introduced in the dilation procedure. We also derive a design method for the same problem but only inexact scheduling parameters are available. A numerical example well demonstrates the effectiveness of our method with respect to the simultaneous design.