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

Tags

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Mathematical Modeling and Probability Theory.
  • Plasma Physics / Magnetohydrodynamics