Dual pairs of generalized Lyapunov inequalities and balanced truncation of stochastic linear systems

TL;DR

This paper explores two methods for balanced truncation of stochastic linear systems, extending deterministic reachability concepts, with one method providing an H-infinity error bound, enhancing stability and performance guarantees.

Contribution

It introduces two generalized Lyapunov inequality approaches for stochastic systems, with one offering a stochastic H-infinity error bound, advancing model reduction techniques.

Findings

Both methods preserve mean-square stability.

Only the second method provides an H-infinity error bound.

The approaches extend deterministic Gramian concepts to stochastic systems.

Abstract

We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the second leads to a stochastic H-infinity-type bound for the approximation error of the truncated system.