Linear Matrix Inequalities for Analysis and Control of Linear Vector Second-Order Systems

Many dynamical systems are modeled as vector second order differential equations. This paper presents analysis and synthesis conditions in terms of Linear Matrix Inequalities (LMI) with explicit dependence in the coefficient matrices of vector second-order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter-dependent Lyapunov functions as certificates of stability of uncertain and time-varying vector second-order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second-order form. Copyrightc 2010 John Wiley & Sons, Ltd.