Piecewise Riccati Equations and the Bounded Real Lemma

This article concerns peicewise 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 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 inequality. We show how these can be converted to matrix inequalities which are linear in the unknowns. Thus modern methods for optimizing such expressions can be used to obtain solutions. ( 1997 by John Wiley & Sons, Ltd.