A family of <i>H</i>_∞ controllers for dissipative Hamiltonian systems

Abstract

SUMMARY Using structure properties of dissipative Hamiltonian systems, this paper investigates the parameterization problem of H infty controllers for such systems. A family of H ∞ controllers with full information is first obtained by interconnecting an H ∞ controller with a generalized zero‐energy‐gradient (ZEG) detectable, free generalized Hamiltonian system. Then, a family of H ∞ controllers with partial information is presented in terms of the solution to an inequality only in 2 n independent variables (twice as many as the one used to characterize the state feedback) and without imposing an additional cascade condition. Both of the parameterization methods avoid solving Hamilton–Jacobi–Issacs equations (or inequalities), and thus the proposed controllers are relatively simple in form and easy in operation. Numerical experiments show the effectiveness and feasibility of the proposed methods. Copyright © 2011 John Wiley &amp; Sons, Ltd.