Antonis Papachristodoulou

TL;DR: The paper provides an overview on sum of squares programming, describes the primary features of SOSToolS, and shows how SOSTOOLS is used to solve sum of square programs.

TL;DR: In this article, a relaxation of Lyapunov's direct method has been proposed to include systems with equality, inequality, and integral constraints, which allows robustness analysis to be performed.

TL;DR: In this paper, the state feedback control synthesis problems for nonlinear systems, either without or with guaranteed cost or H/sub /spl infin// performance objectives, were formulated in terms of state dependent linear matrix inequalities, and Semidefinite programming relaxations based on the sum of squares decomposition were used to efficiently solve such inequalities.

TL;DR: In this article, the authors present stability and robust stability analysis tools for different classes of systems: systems described by nonlinear ordinary differential equations or differential algebraic equations, hybrid systems with nonlinear subsystems and/or nonlinear switching surfaces, and time-delay system described by functional differential equations, and discuss how different analysis questions such as model validation and safety verification can be answered for uncertain nonlinear and hybrid systems.

TL;DR: A unified framework that considers linear MAS models with different feedback delays, e.g. affecting only the neighbor's output, or affecting both the agent's own and its neighbors' output is developed.