Output Feedback Control of Linear Time-Invariant Systems with Operational Constraints

TL;DR

This paper presents a systematic output feedback control design for linear systems with operational constraints, ensuring safety and robustness using theoretical tools like Nagumo's Theorem and Control Barrier Functions.

Contribution

It introduces a continuous piecewise-linear output feedback controller that guarantees constraint satisfaction and robustness margins, applicable to safety-critical systems.

Findings

Guarantees constraint satisfaction using Nagumo's Theorem and the Comparison Lemma.

Provides a robust, analyzable controller suitable for MIMO systems.

Demonstrates practical relevance through aircraft control case studies.

Abstract

This paper introduces a systematic method for designing robust linear controllers using output feedback in the presence of operational constraints. The design uses Nagumo's Theorem and the Comparison Lemma to guarantee constraint satisfaction, while incorporating min-norm optimal control principles inspired by Control Barrier Functions. The resulting controller is a continuous piecewise-linear output feedback policy that preserves the closed-loop system's analyzability using linear systems theory. Due to the linear control design, multi-input multi-output (MIMO) robustness margins can be derived with and without active operational constraints. This paper shows that operational constraints on the system's state can be satisfied using an observer-based output feedback control design. Through flight control trade studies, we demonstrate the practical relevance of the framework in safety-critical aircraft control applications.