Stabilization and disturbance rejection with decay rate bounding in discrete‐time linear parameter‐varying systems via ℋ∞ gain‐scheduling static output feedback control

• Published in: International journal of robust and nonlinear control 2022-09, Vol.32 (14), p.7920-7945
• Main Authors: Sereni, Bruno, Assunção, Edvaldo, Teixeira, Marcelo Carvalho Minhoto
• Format: Article
• Language: English
• Subjects: Control systems design; Controllers; Decay rate; Feedback control; Gain scheduling; gain‐scheduling control; Liapunov functions; Linear matrix inequalities; Lower bounds; LPV discrete‐time systems; Optimization; Output feedback; Parameters; parameter‐dependent Lyapunov functions; Rejection; Stabilization; static output feedback
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.6250

The stabilization of discrete‐time linear parameter‐varying (LPV) systems via gain‐scheduling static output feedback (SOF) control is addressed in this article. We propose new sufficient linear matrix inequalities (LMI) conditions for synthesizing a gain‐scheduled SOF controller that ensures asymptotic stability and also imposes a lower bound on the closed‐loop decay rate. The SOF controller design is based on a two‐step method: a state‐feedback controller is obtained in a first‐stage design, which is then used as input information in the second stage for computing the desired gain‐scheduled SOF controller. The proposed LMI constraints are given in terms of the existence of affine parameter‐dependent Lyapunov functions, considering arbitrarily fast variation of the time‐varying parameters. An extension for coping with disturbance rejection is also proposed, in terms of the H∞$$ {\mathcal{H}}_{\infty } $$ guaranteed cost optimization. Some numerical experiments are presented to illustrate the control synthesis procedure and its efficacy. Also, feasibility analyses are presented to compare and show the advantages of our results over other available strategies present in literature.