Stochastic dissipativity for systems with probabilistic input delays

Published: 01 Jan 2025, Last Modified: 16 May 2025Autom. 2025EveryoneRevisionsBibTeXCC BY-SA 4.0
Abstract: This work considers stochastic operators in Hilbert spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from an operator-theoretic perspective, and the well-known open-loop dissipativity conditions for closed-loop/network stability are extended to the stochastic case. Criteria are derived to identify dissipative nonlinear systems with stochastic input delays, and this result is used to find delay-distribution-dependent linear matrix inequality conditions for stochastic dissipativity of a linear system with input delays of a known probability distribution. A numerical experiment demonstrates the utility of the resulting criteria for robust plant analysis and controller design, highlighting significantly reduced conservatism compared to deterministic methods.
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