Nonlinear HUoControl using SumofSquares Decomposition

Thispaperdiscusses thestate feedback Ho)control foraclass ofnonlinear system basedonitsL2gaincomputation, wherethetechnique ofthesumofsquares decomposition is applied. By reformulating theHamilton-Jacobin inequality as alinear semi-definite optimization problem, theL2gainofthe considered nonlinear systems canbecomputed withtheaidofthe software SOSTOOLS(1)underthesumofsquares framework. A newiterative state feedback Ho)control synthesis algorithm fortheconsidered nonlinear system isproposed, whereastate feedback Ho)controller issynthesized iteratively basedonan initial controller thatcanstabilize thesystem toafinite L2gain. Someexamples areshowntoillustrate theeffectiveness ofthe proposed algorithm. I.INTRODUCTION