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 he used to establish the global stability or the global stability with H_∞ 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 that are numerically feasible with commercially available software. An example is given to illustrate the application of the proposed methods