Inverse system design for LPV systems using biquadratic Lyapunov functions

This paper proposes the analysis and synthesis of inverse systems for linear parameter-varying (LPV) systems using biquadratic Lyapunov functions. The LPV systems are represented with affine matrices of parameters in their state space representations, and the parameters are supposed to be in a known convex region. The proposed analyses for linear time-invariant (LTI) inverse systems and for LPV inverse systems that are represented with affine matrices of parameters in their state space representations are formulated in terms of linear matrix inequalities (LMI) that are affine functions of parameters. The proposed synthesis of full order LPV inverse systems is formulated only in terms of LMI that are affine functions of parameters. Robust full-order inverse system design, that is, full-order LTI inverse system design, is included in our formulation as a special case.