A new MATLAB toolbox for computing eigenvalues and invariant subspaces of Hamiltonian and skew-Hamiltonian matrices is described. Based on orthogonal symplectic decompositions, the implemented algorithms are both numerically backward stable and structure-preserving. It will be demonstrated how this toolbox can be used to address a number of tasks in systems and control theory, including some model reduction methods and the computation of the H ∞ norm. © 2005 IEEE.