Synthesis of controllers for modal shaping in linear parameter-varying systems via the implicit model following formulation

The control synthesis problem involving implicit model following (IMF) is considered in the context of linear parameter-varying (LPV) and H₂/H∞ theories. The well-known quadratic or nominal H₂ IMF problem is first extended to encompass LPV system models with a linear fractional transformation (LFT) structure. This problem is then embedded in the framework of LPV theory. Conditions for dealing with additional mixed H₂/H∞ criteria are discussed. The solvability conditions are provided with little conservatism by a previous multi-channel LFT/LPV result in discrete time. Finally, an illustrative example is used to validate this new formulation. Also. we demonstrate through this example that the IMF formulation is an effective technique to achieve a desired transient behavior for LPV systems.