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Analysis of transient stability of strongly nonlinear post-fault dynamics is one of the most computationally challenging parts of Dynamic Security Assessment. This paper proposes a novel approach for assessment of transient stability of the…

Systems and Control · Computer Science 2017-11-01 Thanh Long Vu , Konstantin Turitsyn

Stability and safety are two important aspects in safety-critical control of dynamical systems. It has been a well established fact in control theory that stability properties can be characterized by Lyapunov functions. Reachability…

Systems and Control · Electrical Eng. & Systems 2022-01-03 Yiming Meng , Yinan Li , Maxwell Fitzsimmons , Jun Liu

We provide several characterizations of convergence to unstable equilibria in nonlinear systems. Our current contribution is three-fold. First we present simple algebraic conditions for establishing local convergence of non-trivial…

Dynamical Systems · Mathematics 2016-11-17 A. N. Gorban , I. Yu. Tyukin , H. Nijmeijer

This article deals with input-to-state stability (ISS) of discrete-time switched systems. Given a family of nonlinear systems with exogenous inputs, we present a class of switching signals under which the resulting switched system is ISS.…

Systems and Control · Computer Science 2017-11-27 Atreyee Kundu , Debasish Chatterjee

We consider scalar-input control systems in the vicinity of an equilibrium, at which the linearized systems are not controllable. For finite dimensional control systems, the authors recently classified the possible quadratic behaviors.…

Optimization and Control · Mathematics 2019-05-27 Karine Beauchard , Frédéric Marbach

This paper considers small gain theorems for the global asymptotic and exponential input-to-state stability for discrete time time-delay systems using Razumikhin-type Lyapunov function. Among other things, unlike the existing literature, it…

Systems and Control · Electrical Eng. & Systems 2023-10-06 Yuanqiu Mo , Wenwu Yu , Huazhou Hou , Soura Dasgupta

In this paper, we study the well-posedness and the input-to-state type stability of a one-dimensional fluid-particle interaction system. A distinctive feature, not yet considered in the ISS literature, is that our system involves a free…

Analysis of PDEs · Mathematics 2025-05-21 Zhuo Xu

In this paper, an asymptotic stability proof for a class of methods for inexact nonlinear model predictive control is presented. General Q-linearly convergent online optimization methods are considered and an asymptotic stability result is…

Optimization and Control · Mathematics 2021-12-01 Andrea Zanelli , Quoc Tran Dinh , Moritz Diehl

This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…

Optimization and Control · Mathematics 2026-03-03 Matthieu Barreau , Carsten W. Scherer , Frederic Gouaisbaut , Alexandre Seuret

This paper presents a small-gain theorem for networks composed of a countably infinite number of finite-dimensional subsystems. Assuming that each subsystem is exponentially input-to-state stable, we show that if the gain operator,…

Optimization and Control · Mathematics 2020-12-02 Christoph Kawan , Andrii Mironchenko , Abdalla Swikir , Navid Noroozi , Majid Zamani

For linear periodic finite-dimensional systems, it is well-known that, first, exponential stability is equivalent to the existence of a unique periodic positive definite solution to the Lyapunov equation, and second, the Lyapunov equation…

Dynamical Systems · Mathematics 2026-05-18 Irina V. Aleksandrova , Juan J. L. Velázquez

In this paper, we propose a new convex approach to stability analysis of nonlinear systems with polynomial vector fields. First, we consider an arbitrary convex polytope that contains the equilibrium in its interior. Then, we decompose the…

Optimization and Control · Mathematics 2014-11-24 Reza Kamyar , Chaitanya Murti , Matthew Peet

Quadratic Lyapunov functions are prevalent in stability analysis of linear consensus systems. In this paper we show that weighted sums of convex functions of the different coordinates are Lyapunov functions for irreducible consensus…

Optimization and Control · Mathematics 2015-01-08 Herbert Mangesius , Jean-Charles Delvenne

This paper discusses the stabilizability, weak stabilizability, exact observability and robust quadratic stabilizability of linear stochastic control systems. By means of the spectrum technique of the generalized Lyapunov operator, a…

Optimization and Control · Mathematics 2023-07-19 Weihai Zhang , Bor-Sen Chen

Many nonlinear dynamical systems can be written as Lure systems, which are described by a linear time-invariant system interconnected with a diagonal static sector-bounded nonlinearity. Sufficient conditions are derived for the global…

Systems and Control · Computer Science 2015-09-07 Kwang-Ki K. Kim , Richard D. Braatz

A controller synthesis method for state- and input-constrained nonlinear systems is presented that seeks continuous piecewise affine (CPA) Lyapunov-like functions and controllers simultaneously. Non-convex optimization problems are…

Systems and Control · Electrical Eng. & Systems 2022-03-08 Reza Lavaei , Leila Bridgeman

A class of distributed systems with a cyclic interconnection structure is considered. These systems arise in several biochemical applications and they can undergo diffusion driven instability which leads to a formation of spatially…

Optimization and Control · Mathematics 2007-05-23 M. R. Jovanovic , M. Arcak , E. D. Sontag

We consider the problem of robust diffusive stability (RDS) for a pair of coupled stable discrete-time positive linear-time invariant (LTI) systems. We first show that the existence of a common diagonal Lyapunov function is sufficient for…

Dynamical Systems · Mathematics 2025-06-23 Blake McGrane-Corrigan , Rafael de Andrade Moral , Oliver Mason

Motivated by the scalability problem in large networks, we study stability of a network of infinitely many finite-dimensional subsystems. We develop a so-called relaxed small-gain theorem for input-to-state stability (ISS) with respect to a…

Dynamical Systems · Mathematics 2020-11-24 Navid Noroozi , Andrii Mironchenko , Fabian R. Wirth

- This article deals with the derivation of ISS-Lyapunov functions for infinite-dimensional linear systems subject to saturations. Two cases are considered: 1) the saturation acts in the same space as the control space; 2) the saturation…

Analysis of PDEs · Mathematics 2017-11-15 Swann Marx , Yacine Chitour , Christophe Prieur