Robust tracking controller design for non-Gaussian singular uncertainty stochastic distribution systems

In this paper, the robust tracking control problem for uncertain singular stochastic distribution control (SDC) systems is considered. A new control target, where the distribution tracking error at each time instant satisfies a certain upper bound beyond a limited time, is proposed. This control target is different from the tracking control in the output SDC systems which makes the output probability density function (PDF) track a desired PDF as close as possible. Then an instant performance index instead of the infinite integration index is adopted, and the upper bound of this index is taken as the stability condition of a Lyapunov function to obtain a robust tracking controller via an augmentation control and linear matrix inequality (LMI). Simulations are also included to show the effectiveness of the proposed algorithm and encouraging results have been obtained.