H∞ control for nonlinear descriptor systems

In this paper, we study the H_∞ control problem for nonlinear descriptor systems governed by a set of differential-algebraic equations (DAEs) of the form Ex˙ = F(x, w, u), z = Z(x, w, u), y = Y(x, w, u), where E is, in general, a singular matrix. 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 DAEs. 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.