Stabilization of polytopic discrete-time varying systems with rate and magnitude saturating actuators and bounded disturbances

• Published in: Journal of the Franklin Institute Vol. 361; no. 10; p. 106915
• Main Authors: Oliveira, Lucas A.L., Leite, Valter J.S., Silva, Luís F.P., Guelton, Kevin
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01-07-2024; Elsevier
• Subjects: Artificial Intelligence; Automatic; Automatic Control Engineering; Computer Science; Dynamical Systems; Engineering Sciences; ISS; LPV systems; Mathematics; Polytopic modeling; Rate saturation; Region of attraction; Saturating actuators; Slew rate; T–S fuzzy; T–S fuzzy; Polytopic modeling; Slew rate; ISS; LPV systems; Region of attraction; Saturating actuators; Rate saturation; T-S fuzzy; Polytopic modeling LPV systems T-S fuzzy Saturating actuators rate saturation slew rate ISS Region of attraction
• ISSN: 0016-0032; 1879-2693
• DOI: 10.1016/j.jfranklin.2024.106915

This study tackles the critical challenge of designing parameter-dependent controllers for the wide class of discrete-time polytopic systems under rate and magnitude saturating actuators. Such a class finds widespread use in diverse applications spanning from medicine to industrial engineering. Our central contribution lies in developing novel convex parameter-dependent state feedback controller synthesis conditions that ensure regional and input-to-state stability, effectively mitigating the adverse effects of rate and magnitude-saturating actuators. Our approach considers the ℓ2/ℓ∞ gain between disturbance input and controlled output, offering performance specifications and retaining validity for specific initial conditions and amplitude-limited input disturbances. Moreover, our methodology is highly adaptable and suitable for a broad spectrum of systems, including LPV/quasi-LPV and T–S fuzzy systems. We leverage the position-type feedback model with speed limitation (PMSL) and the generalized sector condition to derive our controller synthesis method, resulting in a parallel-distributed-compensation strategy under standard assumptions, ensuring practicality and applicability to diverse system requirements. To highlight the effectiveness of our approach, we present numerical examples for comparative evaluation concerning the existing literature. Furthermore, we validate our methodology through real-time experiments conducted on a nonlinear coupled tank system, providing concrete evidence of its efficacy and feasibility for real-world implementation.
•New state feedback controller ensuring local stability with actuator limits and ℓ2/ℓ∞ gain performance.•Polytopic representation for LPV, quasi-LPV, and T–S fuzzy models in saturating control design.•Effects of amplitude-bounded disturbances and region of attraction for closed loop systems.•Optimizing control gains to maximize region of attraction and minimize disturbance impacts.•Real-time control experiments on a nonlinear system using the proposal.