Dual Pairs of Generalized Lyapunov Inequalities and Balanced Truncation of Stochastic Linear Systems

Dual Pairs of Generalized Lyapunov Inequalities and Balanced Truncation of Stochastic Linear Systems

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 ∞ -type bound for the approxim...

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Veröffentlicht in:IEEE transactions on automatic control 2017-02, Vol.62 (2), p.782-791
Hauptverfasser: Benner, Peter, Damm, Tobias, Rodriguez Cruz, Yolanda Rocio
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic mean square stability
Asymptotic stability
balanced truncation
Control systems
generalized Lyapunov equation
Liapunov functions
Linear systems
Mathematical model
model order reduction
Stability criteria
stochastic linear system
Stochastic processes
Stochastic systems
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Zusammenfassung: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 ∞ -type bound for the approximation error of the truncated system.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2016.2572881