Piecewise Riccati equations and the bounded real lemma

This article concerns piecewise linear systems and determining if they meet given H^∞ performance specifications. Such problems occur in control of linear systems with saturation nonlinearities. While one could imagine many mathematically natural piecewise linear systems problems we took care to extract one which does correspond to control of saturated plants. We think many such problems will fall into the category treated here. After a serious compromise (which makes our test for meeting specifications conservative), we arrive at a type of piecewise Riccati equation. Even these look formidable, however we begin a study of them