Differential dissipativity theory for dominance analysis
For control theorists and engineers, it provides a unified framework to analyze low-dimensional dominant behaviors in high-dimensional nonlinear systems, extending classical dissipativity theory.
The paper formalizes the concept of dominance in nonlinear systems using differential analysis, showing it can be studied through linear dissipation inequalities and an interconnection theory that generalizes classical dissipativity-based stability analysis. This enables tractable analysis of multistability (via 1-dominance) and limit cycle oscillations (via 2-dominance).
High-dimensional systems that have a low-dimensional dominant behavior allow for model reduction and simplified analysis. We use differential analysis to formalize this important concept in a nonlinear setting. We show that dominance can be studied through linear dissipation inequalities and an interconnection theory that closely mimics the classical analysis of stability by means of dissipativity theory. In this approach, stability is seen as the limiting situation where the dominant behavior is 0-dimensional. The generalization opens novel tractable avenues to study multistability through 1-dominance and limit cycle oscillations through 2-dominance.