Abstract

This paper addresses L2-gain analysis and robust H∞ control of nonlinear sampled-data systems described by a polynomial linear parameter varying (PLPV) model. The main contributions of this paper are as follows. First, conditions for L2-gain analysis of sampled-data PLPV systems are derived using a modified Krasovskii functional in which the distance between the real and measured parameters are considered as uncertainties. The resulting conditions are formulated in terms of parameterized linear matrix inequalities (PLMI). Second, a solution approach for satisfying PLMI conditions over the set of whole parameters and uncertainties is proposed using the sum-of-squares decomposition method. Third, conditions for robust H∞ sampled-data controller synthesis for nonlinear systems described by PLPV models are derived in terms of parameterized bilinear matrix inequalities (PBMI) with the maximum allowable sampling period as the parameter. To make the resulting bilinear matrix inequality (BMI) problems tractable, an iterative algorithm is developed and utilized to solve the problem. Finally, several real-world examples are provided to demonstrate the effectiveness of the proposed approach.