A dissipativity theorem for p-dominant systems

Forni, F and Sepulchre, R (2018) A dissipativity theorem for p-dominant systems. In: 56th IEEE Conference on Decision and Control, 2017-12-12 to -- pp. 3467-3472..

Abstract

We revisit the classical dissipativity theorem of linear-quadratic theory in a generalized framework where the quadratic storage is negative definite in a p-dimensional subspace and positive definite in a complementary subspace. The classical theory assumes p = 0 and provides an interconnection theory for stability analysis, i.e. convergence to a zero dimensional attractor. The generalized theory is shown to provide an interconnection theory for p-dominance analysis, i.e. convergence to a p-dimensional dominant subspace. In turn, this property is the differential characterization of a generalized contraction property for nonlinear systems. The proposed generalization opens a novel avenue for the analysis of interconnected systems with low-dimensional attractors.