Grid- and transformation-free model order reduction for linear parameter varying systems

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This project considers model order reduction for linear parameter varying (LPV) systems. LPV systems are dynamic systems where the state space matrices are functions of a time-varying parameter vector which is not known in advance but measurable at each time instant. The main advantage of the LPV framework is that it allows to extend linear controller design techniques to nonlinear and time-varying systems, such that analysis and synthesis problems are being solved by solving linear matrix inequalities (LMIs). The computational complexity solving LMIs grows however rapidly with increasing state and parameter dimensions, and model approximation is required when dealing with large scale systems.In this project balanced truncation for LPV models is addressed, and three open problems arising in existing approaches will be solved:- The need of solving LMI conditions on a grid in parameter space will be avoided by developing a grid-free reduction method based on the full-block S-procedure.- The need of parameter-dependent transformations of the model will be avoided by representing the reduction problem as an equivalent fixed-structure controller synthesis problem, leading to a transformation free-reduction procedure. - The open and practically important problem of modal decomposition of LPV models will be addressed by combining the fixed-structure approach above with existing modal matching results.