Robust H∞ control of piecewise-linear chaotic systems with random data loss

This paper studies the problem of robust H∞ control of piecewise-linear chaotic systems with random data loss. The communication links between the plant and the controller are assumed to be imperfect (that is, data loss occurs intermittently, which appears typically in a network environment). The data loss is modelled as a random process which obeys a Bernoulli distribution. In the face of random data loss, a piecewise controller is designed to robustly stabilize the networked system in the sense of mean square and also achieve a prescribed H∞ disturbance attenuation performance based on a piecewise-quadratic Lyapunov function. The required H∞ controllers can be designed by solving a set of linear matrix inequalities (LMIs). Chua's system is provided to illustrate the usefulness and applicability of the developed theoretical results.