# A dissipativity theorem for p-dominant systems

arXiv: https://arxiv.org/abs/1709.06155 · HTML: https://mlsanity.com/paper/1709.06155/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Sep 2017.

## Built on by (most cited first, 1 of 1)

- [On Dominant Manifolds in Reservoir Computing Networks](https://mlsanity.com/paper/2604.05967/) (2026)

## Abstract (arXiv)

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 inter- connection 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.