Adaptive control design of uncertain piecewise-linear systems

In this paper, we study adaptive control design problem of piecewise-linear systems with matching parametric uncertainties. The basic idea is to construct a piecewise control law and a piecewise parameter adaptation law in such a way that a piecewise quadric Lyapunov function can be used to establish the global stability. All of the synthesis conditions are formulated as Linear Matrix Inequities and can therefore be efficiently solved. Moreover, the possibility of sliding motion at the boundary of polytopic regions is considered, and the results are demonstrated by application to control a linear motor.