A Hamilton-Jacobi inequality approach to the strict \(H_ \infty\) control problem of nonlinear systems
The authors study an \(H^\infty\) problem with nonlinear dynamics with respect to the state variable \(x\) but affine with respect to the control variable \(u\). The strict problem of \(H^\infty\) type is studied: to find a constant \(\gamma\) and a controller such that the associated \(\mathbb{L}^2\)-gain is less (strictly) than \(\gamma\). In this paper, conditions of existence of dissipative functions, of feedback control, and of output feedback are studied through suitable Hamilton-Jacobi inequalities for regular functions (at least \(C^1\)).
scientific article; zbMATH DE number 885877