Linear parameter varying (LPV) systems are described by linear dierential equations whose describing matrices depend on time-varying parameters. The goal in synthesis is to design a controller of the very same structure such that the overall controlled system satises certain desired specications on stability and performance for the entire set of permissible parameter trajectories. The implementation of LPV controllers takes on-line measurements of the time-varying parameters into account in order to improve the performance over robust controllers, compensators without any adaptation capabilities.
In this talk, we highlight the challenges in synthesizing controller in order to meet certain desired stability and performance properties. Furthermore, we address a long-standing open problem in robust control and present novel algorithms that allow to systematically reduce conservatism by relying on frequency-dependent stability multipliers. In the nal part of the talk we reveal how the developed framework enables the design of distributed controllers for spatially interconnected systems with reduced conservatism.
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