  Linear parameter varying (LPV) analysis and controller synthesis theory
rooted in the small gain and passivity framework currently exist. The study of
conic systems encompasses both small gain and passivity properties, and herein,
analysis and controller synthesis for polytopic conic systems is considered.
Linear matrix inequality constraints are given to provide conic bounds for
polytopic systems. In addition, given controller conic bounds, a control
synthesis method is introduced. The polytopic conic controller is demonstrated
on a heat exchanger in simulation, and compared to existing LPV control design
techniques.
