Dissipativity theory for discrete‐time nonlinear stochastic dynamical systems
Abstract
In this paper, we develop stochastic dissipativity theory for discrete‐time nonlinear dynamical systems expressed by Itô‐type difference equations using basic state properties. Specifically, a stochastic version of dissipativity and losslessness using a state dissipation inequality in expectation for controlled Markov chains is presented. The results are then used to derive extended Kalman–Yakubovich–Popov conditions for characterizing stochastic dissipativity and losslessness in terms of the nonlinear system functions using continuous storage functions. Finally, feedback interconnection stability in probability results are developed generalizing the small gain and positivity theorems to discrete‐time stochastic systems.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 20, 2022
- Source ID
- 10.1002/rnc.6139
Entities
People
- Manuel Lanchares
- Wassim M. Haddad
Organizations
- Air Force Office of Scientific Research
- Georgia Tech