L2‐disturbance attenuation for LPV systems under sampled‐data control

• Published in: International journal of robust and nonlinear control 2018-11, Vol.28 (16), p.5019-5032
• Main Authors: Gomes da Silva Jr, J.M., Palmeira, A.H.K., Moraes, V.M., Flores, J.V.
• Format: Article
• Language: English
• Subjects: Attenuation; Computational geometry; Convexity; L2‐gain; linear matrix inequality (LMI); linear parameter varying (LPV) systems; Mathematical models; Optimization; Parameter varying control; sampled‐data control; Sampling; Upper bounds
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.4297

Summary This paper focuses on the synthesis of sampled‐data linear parameter‐varying (LPV) control laws. In particular, the problem of L2 disturbance attenuation for continuous‐time LPV systems under aperiodic sampling is addressed. It is explicitly assumed that the LPV controller is updated only at the sampling instants while the plant parameter can evolve continuously between two sampling instants. The proposed approach is based on a polytopic model for the LPV system and the use of a parameter‐dependent looped‐functional to deal with the aperiodic sampling effects. From these ingredients, conditions in a quasi‐LMI form (ie, they are LMIs provided a scalar parameter is fixed) are derived to compute a stabilizing control law ensuring an upper bound on the closed‐loop system L2‐gain. These conditions are then incorporated to convex optimization problems aiming at either minimizing the L2‐gain upper bound or maximizing the allowable sampling interval for which stability is ensured. Numerical examples illustrate the proposed methodology.