Dissipativity Theory for Discrete-Time Nonlinear Stochastic Dynamical Systems, Part I: Input-Output and State Properties

Dissipativity theory for discrete‐time nonlinear stochastic dynamical systems

“…These results generalize the feedback interconnection stability results of Reference 24, and in the case where the supply rate involves the net system power or weighted input–output energy, these results provide extensions of the classical positivity and small gain theorems to discrete‐time stochastic dynamical systems. Finally, we note that a preliminary conference version of this paper appeared in Reference 25. The present paper considerably expands on Reference 25 by providing detailed proofs of all of the results in Reference 25, developing Kalman–Yakubovich–Popov conditions and stability of feedback interconnection results, providing additional discussion, and giving several numerical examples.…”

“…Finally, we note that a preliminary conference version of this paper appeared in Reference 25. The present paper considerably expands on Reference 25 by providing detailed proofs of all of the results in Reference 25, developing Kalman–Yakubovich–Popov conditions and stability of feedback interconnection results, providing additional discussion, and giving several numerical examples.…”

Nonlinear–nonquadratic optimal and inverse optimal control for discrete‐time stochastic dynamical systems

“…Future research will focus on extending these results to stochastic optimal control problems guaranteeing gain, sector, and disk margins for discrete-time nonlinear stochastic dynamical systems controlled by nonlinear optimal and inverse optimal regulators that minimize a nonlinear-nonquadratic performance criterion. Furthermore, connections between discrete-time stochastic dissipativity 30 and optimality of discrete-time nonlinear stochastic systems will also be explored. Finally, extensions to stochastic systems with time delays and impulsive effects will also be explored.…”