IMPROVED ADAPTIVE H∞ CONTROLLER SYNTHESIS OF PIECEWISE-AFFINE SYSTEMS

This paper considers the adaptive H-infinity control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection-type piecewise adaptive law, the problem of the adaptive H-infinity control of PWS can be reduced to the H-infinity control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability and H-infinity performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.