Reduced Order Positive Filter Design for Positive Uncertain Discrete-Time Linear Systems

Author(s)

Spagolla, Amanda ^[1] ; Morais, Cecilia F. ^[2] ; Oliveira, Ricardo C. L. F. ^[1] ; Peres, Pedro L. D. ^[1]

Affiliation

^[1] Univ Campinas UNICAMP, Sch Elect & Comp Engn, BR-13083852 Campinas, SP - Brazil

^[2] Pontifical Catholic Univ Campinas, Ctr Exact Environm & Technol Sci, BR-13087571 Campinas, SP - Brazil

• Document type: Journal article
• Source: IEEE CONTROL SYSTEMS LETTERS; v. 6, p. 1148-1153, 2022.
• Web of Science Citations: 0

Abstract

The problems of reduced order H-2 and H-infinity positive filter design for positive uncertain discrete-time linear systems are investigated in this letter. Due to the positivity constraint on the matrices of the filter, optimal H-2 and H-infinity filters cannot be obtained through standard linear matrix inequality (LMI) methods, even in the context of full order filtering for precisely known systems. Therefore, new sufficient LMI conditions are proposed for H-2 and H-infinity positive filter design for positive discrete-time linear systems, having as main advantage the fact that the filter matrices are variables of the problem. In this case, no structural constraints on the optimization variables (source of conservativeness) are needed to ensure positivity. Thanks to a relaxation in the stability of the filter, an iterative algorithm with a feasible initial condition is proposed, allowing the search for positive filters that assure an H-2 or H-infinity guaranteed attenuation level for the filtered system. The conditions can deal with full or reduced order filtering, polytopic type uncertainty and structural constraints. Examples inspired on models borrowed from the literature illustrate the results. (AU)

• FAPESP's process: 19/09363-5 - Control of uncertain positive linear systems by means of linear matrix inequalities
• Grantee: Amanda Spagolla
• Support type: Scholarships in Brazil - Doctorate