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Synthesis of LPV controllers with reduced implementation complexity

The application of linear parameter-varying (LPV) control techniques proves difficult when the number of scheduling parameters is large. This paper reviews and extends practical methods for linear fractional transformation (LFT) based LPV controller design, in order to achieve reduced implementation complexity via affine parameter dependence. Methods to approximate a given affine LPV model are reinterpreted in terms of a nonlinear mapping from rational to reduced affine parameter dependence and a procedure is proposed, that does not rely on experimental data and is therefore also applicable to unstable systems. It is further proposed, to evaluate multiplier conditions by taking into account rational dependence of affine parameters on LFT parameters via a secondary application of the full-block S-procedure. Numerical examples illustrate that the proposed methods can result in reduced conservatism, implementation and synthesis complexity.