October 8, 2025Open Access

Output Feedback Design for Parameter Varying Systems subject to Persistent Disturbances and Control Rate Constraints

JEJackson G. ErnestoPolydoro Ernani de São Thiago University Hospital ECEugênio B. CastelanUniversidade Federal de Santa Catarina WLWalter LúciaConcordia University

Key Points

The proposed output feedback controller ensures closed-loop trajectories converge to a smaller set, regardless of disturbances.
Using bilinear optimization, the approach formulates control gains and sets defined by algebraic conditions.
The technique utilizes robust positively invariant sets to manage state and control amplitude constraints effectively.
Numerical examples validate the effectiveness of the proposed design in addressing specified control and disturbance challenges.

Abstract

This paper presents a technique for designing output feedback controllers for constrained linear parameter-varying systems that are subject to persistent disturbances. Specifically, we develop an incremental parameter-varying output feedback control law to address control rate constraints, as well as state and control amplitude constraints. The proposal is based on the concept of robust positively invariant sets and applies the extended Farkas' lemma to derive a set of algebraic conditions that define both the control gains and a robust positively invariant polyhedron that satisfies the control and state constraints. These algebraic conditions are formulated into a bilinear optimization problem aimed at determining the output feedback gains and the associated polyedral robust positively invariant region. The obtained controller ensures that any closed-loop trajectory originating from the polyhedron converges to another smaller inner polyhedral set around the origin in finite time, where the trajectory remains ultimately bounded regardless of the persistent disturbances and variations in system parameters. Furthermore, by including the sizes of the two polyhedral sets inside the objective function, the proposed optimization can also jointly enlarge the outer set while minimizing the inner one. Numerical examples are presented to demonstrate the effectiveness of our proposal in managing the specified constraints, disturbances, and parameter variations.

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