Abstract
This paper revisits the problem of estimating the domain of attraction and the nonlinear L2 gain of a saturated system with an algebraic loop. A max quadratic Lyapunov function, the maximum function of a group of quadratic Lyapunov functions, is proposed for use in the stability and performance analysis for a saturated system. The max quadratic Lyapunov function involves a partitioning of the state space. Exploiting the special properties of regions of the state space, we propose in this paper an enhanced max quadratic Lyapunov function, which results from adding a term that characterizes the regions of the state space to the max quadratic Lyapunov function. The matrix associated with the enhanced max quadratic Lyapunov function is not required to be positive definite, and thus a set of less conservative stability and performance conditions are established, from which a larger estimate of the domain of attraction and a tighter estimate of the nonlinear L2 gain can be obtained. Simulation results indicate the effectiveness and superiority of the proposed method.
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