Controller design and analysis of uncertain piecewise-linear systems

This paper presents controller design and analysis methods for uncertain piecewise-linear systems based on a piecewise-smooth Lyapunov function. The basic idea of the proposed approaches is to construct controllers for the uncertain piecewise-linear systems in such a way that a piecewise-continuous Lyapunov function can be used to establish the global stability or the global stability with H(infinity) performance of the resulting closed loop control systems. It is shown that the control laws can be obtained by solving a set of linear matrix inequalities (LMI) that are numerically feasible with commercially available software. An example is given to illustrate the application of the proposed methods.