## Improved perturbation bounds for the continuous-time $H_{\infty}$-control problem

Nicolai D. Christov, Mihail M. Konstantinov, and Petko Hr. Petkov

### Abstract

New local perturbation bounds for the continuous-time $H_{\infty}$-control problem are obtained, which are nonlinear functions of the data perturbations and are tighter than the existing condition number-based local bounds. These nonlinear local bounds are then incorporated into nonlocal perturbation bounds which are less conservative than the existing nonlocal perturbation estimates for the $H_{\infty}$-control problem.

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### Key words

$H_{\infty}$-control, perturbation analysis, Riccati equations

### AMS subject classifications

93B36, 65F35, 93B35

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