# Optimal stabilization of linear stochastic systems

## Abstract

Having introduced and motivated our concepts of stochastic control systems in the previous chapter we now turn to optimal and suboptimal stabilization problems.

A classical problem in optimal control theory is the so-called linear quadratic (LQ-)stabilization problem. Among all controls that stabilize a given system, one determines the one that satisfies a certain quadratic nonnegative semidefinite cost-functional. This will be the topic of the first section.

The same techniques used to find an LQ-optimal stabilization can also be applied to identify a worst-case perturbation of a control system. This leads to the Bounded Real Lemma, which is the topic of Section 2.2. The Bounded Real Lemma itself, is the main tool needed to tackle the disturbance attenuation problem in Section 2.3.

## Keywords

Riccati Equation Disturbance Attenuation Optimal Stabilization Perturbation Operator Dynamic Output Feedback## Preview

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