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Learn how to integrate discrete behavior into continuous-time models using synchronous systems in ModelingToolkit through this 14-minute conference talk from JuliaCon Global 2025. Discover the challenges of adding discrete components like friction states and clutch positions to continuous models, and explore how traditional imperative affects and manual functions limit compositionality and reusability. Examine the integration of synchronous systems inspired by Lustre and Lucid Synchrone, which enables discrete behavior description through algebraic clocked discrete-time components. Understand how synchronous components achieve compositionality through connectors and invocations similar to existing continuous-time components, while compiling to efficient imperative code. Master the development of compositional discrete-time systems that function both as standalone systems and integrated components within continuous-time ModelingToolkit models, particularly valuable for digital control systems and hybrid modeling applications.
