On Existence of Solutions to Structured Lyapunov Inequalities
St John’s College, Oxford（牛津大学圣约翰学院）；Department of Engineering Science, University of Oxford（牛津大学工程科学系）；University of Oxford（牛津大学）；Montefiore Institute, University of Liège（列日大学蒙特菲奥研究所）
Aviar Sootla, James Anderson
备注：
To appear in the Proceedings of the 2016 American Control Conference
In this paper, we derive sufficient conditions on drift matrices under which block-diagonal solutions to Lyapunov inequalities exist. The motivation for the problem comes from a recently proposed basis pursuit algorithm. In particular, this algorithm can provide approximate solutions to optimisation programmes with constraints involving Lyapunov inequalities using linear or second order cone programming. This algorithm requires an initial feasible point, which we aim to provide in this paper. Our existence conditions are based on the so-called $\mathcal{H}$ matrices. We also establish a link between $\mathcal{H}$ matrices and an application of a small gain theorem to the drift matrix. We finally show how to construct these solutions in some cases without solving the full Lyapunov inequality.
On Structured Lyapunov Functions and Dissipativity in Interconnected LTI Systems
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb（萨格勒布大学机械与船舶工程学院）；Department of Mathematics, Faculty of Science, University of Zagreb（萨格勒布大学理学院数学系）
Dissipativity properties of a class of nonlinear time-delay systems via Bessel-Legendre inequalities
Hassan II University of Casablanca（卡萨布兰卡哈桑二世大学）；University of Wuppertal（伍珀塔尔大学）；Fraunhofer IEG, Fraunhofer Research Institution for Energy Infrastructures and Geotechnologies IEG（弗劳恩霍夫能源基础设施和岩土技术研究所IEG）
The Popov's Algorithm with Optimal Bounded Stepsize for Generalized Monotone Variational Inequalities
Faculty of Applied Sciences, HCMC University of Technology and Engineering（胡志明市技术与工程学院应用科学学院）；Faculty of Basic Sciences, Van Lang University（文郎大学基础科学学院）；School of Mathematical Sciences, University of Southampton（南安普顿大学数学科学学院）
