Design Automation for Embedded Systems

, Volume 20, Issue 2, pp 95–126 | Cite as

Verification of fixed-point digital controllers using direct and delta forms realizations

  • Iury V. BessaEmail author
  • Hussama I. Ismail
  • Lucas C. Cordeiro
  • João E. C. Filho


The extensive use of fixed-point digital controllers demands a growing effort to prevent design errors that appear in the discrete-time domain. The present article describes a novel verification methodology, which employs bounded model checking (BMC) based on satisfiability modulo theories (SMT) to verify the occurrence of the design errors, because of the finite word-length (FWL) format, in fixed-point digital controllers. Here, the performance realizations of the digital controllers realizations that use delta operators are compared to those that use traditional direct forms. The experimental results show that the delta-form realization substantially reduces the digital controllers’ fragility when compared to the direct-form realization. Additionally, the proposed methodology can be very effective and efficient to verify real-world digital controllers, where conclusive results are obtained in nearly 98 % of the benchmarks.


Fixed-point digital controllers Direct and delta forms Formal methods Bounded model checking 



Part of the results presented in this paper were obtained with the project for research and human resources qualification, for under- and post-graduate levels, in the areas of industrial automation, mobile devices software, and Digital TV, sponsored by Samsung Eletrônica da Amazônia Ltda, under the terms of Brazilian Federal Law number 8.387/91. This research was also supported by CNPq 475647/2013-0 and FAPEAM 062.01722/2014 grants.

Compliance with ethical standards

Conflicts of interest

The authors declare they have no conflict of interest.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Iury V. Bessa
    • 1
    Email author
  • Hussama I. Ismail
    • 1
  • Lucas C. Cordeiro
    • 2
  • João E. C. Filho
    • 2
  1. 1.Graduate Program in Electrical EngineeringFederal University of AmazonasManausBrazil
  2. 2.Electronic and Information Research CenterFederal University of AmazonasManausBrazil

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