David A.W. Barton david.barton.99@bristol.ac.uk

<H3>Explicit periodic solutions in a model of a relay controller with 
delay and forcing}</H3>

We use a combination of numerical and analytical methods to find and 
construct solutions of a model of relay control, formulated as a 
piecewise-constant delay differential equation (DDE). Numerical solutions of 
a related equation, where the discontinuities of the original DDE are smoothed, 
are used to guide the construction of explicit solutions of the original DDE. 
Conversely, the construction of explicit solutions provides 
starting data for numerical continuation of the smoothed equation.