ℋ∞ control for nonlinear differential-algebraic equations

In this paper, we study the ℋ_∞ control problem for nonlinear differential-algebraic equations (DAE). Necessary and sufficient conditions are derived for the existence of a controller solving the problem. We first give various sufficient conditions for the solvability of ℋ_∞ control problem for DAE. Both state feedback and output feedback cases are considered. Then, necessary conditions for the output feedback control problem to be solvable are obtained in terms of two Hamilton-Jacobi inequalities plus a weak coupling condition. Moreover, a parameterization of a family of output feedback controllers solving the problem is also provided