Synthesis of anisotropic suboptimal controllers by convex optimization

TL;DR

This paper develops a convex optimization approach to synthesize anisotropic suboptimal controllers for discrete-time systems affected by uncertain stochastic disturbances, ensuring stability and performance bounds.

Contribution

It introduces a method to design fixed-order output-feedback controllers that handle statistical uncertainties using anisotropic norms and convex optimization techniques.

Findings

Successfully stabilizes systems under uncertain disturbances.

Achieves disturbance attenuation with prescribed anisotropic norm bounds.

Provides a systematic synthesis method for anisotropic controllers.

Abstract

This paper considers a disturbance attenuation problem for a linear discrete time invariant system under random disturbances with imprecisely known probability distributions. The statistical uncertainty is measured in terms of relative entropy 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. The designed anisotropic suboptimal controller generally is a dynamic fixed-order output-feedback compensator which is required to stabilize the closed-loop system and keep its anisotropic norm below a prescribed threshold value.