A Hoare Logic for Single-Input Single-Output Continuous-Time Control Systems
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.
KeywordsTransfer Function Phase Shift Predicate Logic Hybrid Automaton Sequencing Rule
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