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

ABSTRACT This paper develops a framework for designing output feedback controllers for constrained linear parameter‐varying systems that experience persistent disturbances. We specifically propose an incremental parameter‐varying output feedback control law to address control rate constraints, as well as state and control amplitude constraints. This control law provides additional degrees of freedom compared to previous contributions in the literature, offering the potential for improved results in constrained control design. Our approach is based on the concept of robust positively invariant sets. We apply the extended Farkas' lemma to derive a set of algebraic conditions that define both the control gains and a robust positively invariant polyhedron that adheres to the control and state constraints. These algebraic conditions are formulated into a bilinear optimization problem, which aims to determine the output feedback gains and the associated polyhedral robust positively invariant region. The controller obtained ensures that any closed‐loop trajectory starting from the polyhedron converges to a smaller inner polyhedral set around the origin in a finite amount of time. This trajectory remains ultimately bounded, irrespective of the persistent disturbances and variations in system parameters. Furthermore, by incorporating the sizes of the two polyhedral sets into the objective function, our proposed optimization can simultaneously enlarge the outer set while minimizing the inner one. We present numerical examples and comparisons to demonstrate the effectiveness of our proposal in managing the specified constraints, disturbances, and parameter variations.