H 1 Control of Nonlinear Systems: a Convex Characterization

The so-called nonlinear H 1-control problem in state space is considered with an emphasis on developing machinery with promising computational properties. Both state feedback and output feedback H 1-control problems for a class of nonlinear systems are characterized in terms of continuous positive deenite solutions of algebraic nonlinear matrix inequalities which are convex feasibility problems. The issue of existence of solutions to these nonlinear matrix inequalities (NLMIs) is justiied.