About Adaptive Singular Systems with External Delay

TL;DR

This paper develops a robust adaptive control method for singular linear systems with external delays, ensuring stability and controllability through pole-placement and parameter estimation techniques.

Contribution

It introduces a novel adaptive control law for singular systems with delays, incorporating dead zones and detailed analysis of controllability via Weierstrass canonical form.

Findings

Stable adaptive control achieved for systems with external delays

Incorporation of dead zones enhances robustness against disturbances

Detailed controllability conditions via Weierstrass form

Abstract

This paper is mainly concerned with the robustly stable adaptive control of single-input single-output impulse-free linear time-invariant singular dynamic systems of known order and unknown parameterizations subject to single external point delays. The control law is of pole-placement type and based on input/output measurements and parametrical estimation only. The parametrical estimation incorporates adaptation dead zones to prevent against potential instability caused by disturbances and unmodeled dynamics. The Weierstrass canonical form is investigated in detail to discuss controllability and observability via testable conditions of the given arbitrary state-space realization of the same order.