H∞ control of piecewise-linear systems under unreliable communication links

This paper considers the problem of H∞ control of piecewise-linear control systems under unreliable communication links. Due to the limited bandwidth of the channels, signal transmission delays and data packet losses can occur between the plant and the controller. In the presence of random signal transmission delays and data packet losses, a piecewise controller is designed to stabilize the piecewise-linear system in the sense of mean square and also achieve a prescribed H∞ disturbance attenuation performance based on piecewise-quadratic Lyapunov-Krasovskii functionals. It is shown that the H∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Moreover, the controller design method is further extended to uncertain case where the system matrices' uncertainties are represented in polytopic frameworks. Finally, an example is provided to illustrate the effectiveness of the developed theoretical results. © Springer Science+Business Media, LLC 2011.