Robust stability, H-2 and H-infinity guaranteed costs for discrete time-varying uncertain linear systems with constrained parameter variations

Author(s)

Bertolin, Ariadne L. J. ; Peres, Pedro L. D. ; Oliveira, Ricardo C. L. F. ; IEEE

• Document type: Journal article
• Source: 2019 AMERICAN CONTROL CONFERENCE (ACC); v. N/A, p. 6-pg., 2019-01-01.

Abstract

This paper is concerned with the problems of robust stability analysis and computation of H-2 or H-infinity (l(2)-gain) guaranteed costs for discrete-time linear systems with time-varying parameters. Two cases are investigated: i) the time-varying parameters are assumed to belong to a known interval and to have bounded rates of variation; ii) the time-varying parameters follow a known dynamics that can be represented through a discrete-time state space equation. A Lyapunov function that depends on the uncertain matrix of the system up to a certain degree kappa - 1 provides certificates for robust stability and guaranteed costs that can be cast as linear matrix inequality optimization problems, with sharper results as k increases. Numerical examples illustrate that the proposed conditions can be more accurate than other techniques from the literature with lower complexity. (AU)

• FAPESP's process: 17/18785-5 - Parameter-Dependent Linear Matrix Inequalities Applied to Stability Analysis and Synthesis of Controllers and Filters for Uncertain Dynamic Systems
• Grantee: Pedro Luis Dias Peres
• Support Opportunities: Regular Research Grants
• FAPESP's process: 16/22020-1 - Robust stability of uncertain time-varying discrete-time systems by means of linear matrix inequalities
• Grantee: Ariádne de Lourdes Justi Bertolin
• Support Opportunities: Scholarships in Brazil - Master