Dissipation inequalities for a class of composite nonlinear systems, with application to constrained disturbance attenuation

We study problems of disturbance attenuation (with local internal stability), for a class of nonlinear systems. One of the purposes of this paper is to show how the existence of a positive definite solution for the Hamilton-Jacobi-Isaacs inequality can be related to the existence of a solution of the (simpler) Hamilton-Jacobi-Isaacs inequality arising in the problem of disturbance attenuation for the plant. This relation will be demonstrated in the next section, where we will prove a result which, to a limited extent, generalizes a major result on the existence of solutions of the Riccati inequalities arising in the study of the H_∞ suboptimal control problem for linear systems. Then, we will show how this extension can be used in order to generalize the results to H_∞ suboptimal control problem with steady-state constraints for linear systems