A convex formulation of strict anisotropic norm bounded real lemma
Provides a convex optimization framework for analyzing disturbance attenuation in stochastic systems with statistical uncertainty, addressing a known bottleneck in robust control theory.
This paper extends the H-infinity Bounded Real Lemma to stochastic systems with imprecisely known probability distributions, deriving a convex formulation (Strict Anisotropic Norm Bounded Real Lemma) that enables efficient computation of the anisotropic norm via convex optimization.
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.