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.

Stability analysis for stochastic time‐delayed systems allowing admissible edge‐dependent switching signals

“…Stochastic hybrid system is a momentous class of nonlinear systems. Many engineering fields can be modeled as stochastic structure in References 1‐7. For example, the authors studied stochastic delayed hybrid systems with Lévy noise in Reference 5.…”

Robust stabilization and adaptive H∞ control of nonlinear singular systems via static output feedback

“…24–27 In general, there are two approaches to solve nonlinear H ∞ control problems: one is based on Hamiltonian function method in Lu et al 24 and differential game theory in Soravia, 28 and the other is based on the real bounded lemma developed in Chen and Nurdin 29 and Haddad and Lanchares. 30 Dissipation matrix approach is developed in Sun et al 12,31 based on Hamiltonian function method, and it has more extensively application in the control design of NSSs because the approach does not need to decompose the state of NSSs. In this article, the SOF controllers are designed by the state non-decomposition method for NSSs.…”