Journal
IEEE CONTROL SYSTEMS LETTERS
Volume 6, Issue -, Pages 1148-1153Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/LCSYS.2021.3089368
Keywords
Positive discrete-time linear systems; positive filters; H-2 norm; H-infinity norm; linear matrix inequalities
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Funding
- Sao Paulo Research Foundation (FAPESP), SP, Brazil [2019/09363-5]
- Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior (CAPES), Brazil [001]
- CNPq, Brazil
- Fundacao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) [19/09363-5] Funding Source: FAPESP
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This letter investigates the problems of reduced order H-2 and H-infinity positive filter design for positive uncertain discrete-time linear systems. It proposes new LMI conditions which treat the filter matrices as variables, solving the issue of not being able to obtain optimal filters through standard LMI methods under the positivity constraint.
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.
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