Extended-space control design with parameter-dependent Lyapunov functions

This paper addresses a new framework of control design in which controllers are designed in extended spaces rather than in those spaces where the design problems were originally given. The inverse use of the "elimination lemma" can explore this framework and allows us to use parameter-dependent Lyapunov functions. For continuous-time systems, multi-objective control, robust control against polytopic uncertainties and gain-scheduled control for linear parameter-varying systems are considered. An illustrated example is included