Estimating the region of attraction for large-scale systems with uncertainties

In this paper, a new approach is proposed for estimating regions of attraction for large-scale dynamic systems. In designing control laws for such systems, it is essential to incorporate the underlying information structure constraints while keeping the number of optimization variables at a minimum. The proposed method successfully accomplishes both of these objectives. It is computationally efficient, and can produce decentralized control laws without imposing structural constraints on the Lyapunov function (a feature that can considerably improve the quality of the estimate). The design algorithm is based on linear matrix inequalities and can easily accommodate various types of uncertainties in the system model. An example with 300 states is provided to demonstrate the suitability of this approach for large, sparse systems.