A convex formulation of strict anisotropic norm bounded real lemma

TL;DR

This paper extends the H-infinity Bounded Real Lemma to stochastic systems with uncertain distributions, introducing a convex formulation for computing the anisotropic norm using linear matrix inequalities.

Contribution

It provides a convex reformulation of the strict anisotropic norm bounded real lemma, enabling efficient computation via convex optimization techniques.

Findings

Derived a state-space criterion for bounded anisotropic norm.

Reformulated conditions as convex optimization problems.

Enabled efficient computation of anisotropic norm.

Abstract

This paper is aimed at extending the H-infinity Bounded Real Lemma to stochastic systems under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in entropy theoretic terms using the mean anisotropy functional. The disturbance attenuation capabilities of the system are quantified by the anisotropic norm which is a stochastic counterpart of the H-infinity norm. A state-space sufficient criterion for the anisotropic norm of a linear discrete time invariant system to be bounded by a given threshold value is derived. The resulting Strict Anisotropic Norm Bounded Real Lemma involves an inequality on the determinant of a positive definite matrix and a linear matrix inequality. It is shown that slight reformulation of these conditions allows the anisotropic norm of a system to be efficiently computed via convex optimization.