LQ-optimal Sample-data Control under Stochastic Delays: Gridding Approach for Stabilizability and Detectability

TL;DR

This paper addresses LQ optimal control for sampled-data systems with stochastic delays, proposing a gridding approach that ensures stabilizability and detectability through Riccati equations and linear matrix inequalities.

Contribution

It introduces a novel method for stabilizing and detecting stochastic delay systems using Riccati equations and LMI-based conditions, applicable to Markov jump system equivalents.

Findings

Efficient computation of optimal controllers via Riccati difference equations.

Linear matrix inequalities provide sufficient conditions for stabilizability and detectability.

The approach enables design of controllers and observers for stochastic delay systems.

Abstract

We solve a linear quadratic optimal control problem for sampled-data systems with stochastic delays. The delays are stochastically determined by the last few delays. The proposed optimal controller can be efficiently computed by iteratively solving a Riccati difference equation, provided that a discrete-time Markov jump system equivalent to the sampled-data system is stochastic stabilizable and detectable. Sufficient conditions for these notions are provided in the form of linear matrix inequalities, from which stabilizing controllers and state observers can be constructed.