Dilated LMI based LPV control and its application to an aero-engine

This paper proposes a new set of linear matrix inequalities (LMIs) to design dynamic gain scheduled controller for linear systems with time-varying parameters. The proposed LMIs do not involve product terms of the plant state matrices and the Lyapunov matrix. It has been shown that these LMIs can further be extended to accommodate a parameter dependent Lyapunov (PDL) function in an H8 norm based minimization framework. It is found that the LMIs, for the PDL case, are easier to solve if system A-matrix has an affine structure. Moreover, the linear parameter varying (LPV) controller obtained by the proposed LMIs do not require a derivative feedback of the scheduling parameter and hence is more practically implementable than the one obtained by existing proposed LMIs. The proposed method is then applied to a Rolls Royce Spey engine using a mixed sensitivity approach. The non-linear closed loop simulations show that all the required performance objectives are satisfied.