An LMI approach for robust stabilization of aperiodic uncertain sampled-data systems

Author(s)

Morais, Cecilia F. ; Braga, Marcio F. ; Tognetti, Eduardo S. ; Oliveira, Ricardo C. L. F. ; Peres, Pedro L. D. ; IEEE

• Document type: Journal article
• Source: 2017 IEEE 56TH ANNUAL CONFERENCE ON DECISION AND CONTROL (CDC); v. N/A, p. 6-pg., 2017-01-01.

Abstract

The aim of this paper is to investigate the problem of robust stabilization of aperiodic uncertain sampled-data linear systems. Using an impulsive system representation, synthesis conditions are proposed in terms of parameter-dependent linear matrix inequalities (LMIs). Differently from the existing approaches, the resulting state-feedback control gain is not obtained directly from the Lyapunov matrix, easing the task of imposing particular structures to the controller, such as decentralization. Moreover, using a convenient change of variables, a more efficient polynomial approximation is proposed to solve the parameter-dependent LMIs when compared to sum-of-square techniques. An extension to deal with uncertain sampled-data linear systems with periodic sampling interval based on parameter-dependent Lyapunov matrices is also proposed. Numerical examples illustrate the applicability, the advantages, and how the conservativeness of the conditions can be reduced by employing polynomial parameter-dependent decision variables in the proposed conditions when compared with standard approaches from the literature. (AU)

• FAPESP's process: 14/22881-1 - Control of switched systems, Markov jump linear systems and other classes of hybrid systems through LMIs
• Grantee: Cecília de Freitas Morais
• Support Opportunities: Scholarships in Brazil - Post-Doctoral