Differential Dissipativity Theory for Dominance Analysis
Sepulchre, R https://orcid.org/0000-0002-7047-3124
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.
Online Publication Date
Nonlinear control systems, interconnected systems, linear matrix inequalities, linearization techniques, limit-cycles
IEEE Transactions on Automatic Control
Institute of Electrical and Electronics Engineers (IEEE)
European Research Council (670645)