A Hoare Logic for Single-Input Single-Output Continuous-Time Control Systems

  • Richard J. Boulton
  • Ruth Hardy
  • Ursula Martin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2623)


This paper presents a Hoare-style logic for reasoning about the frequency response of control systems in the continuous-time domain. Two properties, the gain (amplitude) and phase shift, of a control system are considered. These properties are for a sinusoidal input of variable frequency. The logic operates over a simplified form of block diagram, including arbitrary transfer functions, feedback loops, and summation of signals. Reasoning is compositional, i.e. properties of a system can be deduced from properties of its subsystems. A prototype tool has been implemented in a mechanised theorem prover.


Transfer Function Phase Shift Predicate Logic Hybrid Automaton Sequencing Rule 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Richard J. Boulton
    • 1
  • Ruth Hardy
    • 1
  • Ursula Martin
    • 1
  1. 1.School of Computer ScienceUniversity of St AndrewsScotlandUK

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