Related papers: Nagumo-Type Characterization of Forward Invariance…
In this paper, we obtain sufficient and necessary conditions of some classical convex sets as positively invariant sets for a continuous dynamical system, namely positive invariance conditions. The approach is based on Nagumo Theorem by…
This paper studies set invariance and contractivity in hybrid systems modeled by hybrid inclusions using barrier functions. After introducing the notion of a multiple barrier functions, we investigate the tightest possible sufficient…
In this paper, tools to study forward invariance properties with robustness to dis- turbances, referred to as robust forward invariance, are proposed for hybrid dynamical systems modeled as hybrid inclusions. Hybrid inclusions are given in…
This article presents tools for the design of control laws inducing robust controlled forward invariance of a set for hybrid dynamical systems modeled as hybrid inclusions. A set has the robust controlled forward invariance property via a…
We provide Lyapunov-like characterizations of boundedness and convergence of non-trivial solutions for a class of systems with unstable invariant sets. Examples of systems to which the results may apply include interconnections of stable…
Recently, Horv\'ath, Song, and Terlaky [\emph{A novel unified approach to invariance condition of dynamical system, submitted to Applied Mathematics and Computation}] proposed a novel unified approach to study, i.e., invariance conditions,…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
We present a framework based on interval analysis and monotone systems theory to certify and search for forward invariant sets in nonlinear systems with neural network controllers. The framework (i) constructs localized first-order…
In this paper we propose a finite-dimensional and deterministic approach to the study of invariant sets of certain nonautonomous differential inclusions naturally arising in the context of random and control dynamical systems, as well as in…
Using the framework of Nambu's generalised mechanics, we obtain a new description of constrained Hamiltonian dynamics, involving the introduction of another degree of freedom in phase space, and the necessity of defining the action integral…
We revisit the problem of computing (robust) controlled invariant sets for discrete-time linear systems. Departing from previous approaches, we consider implicit, rather than explicit, representations for controlled invariant sets.…
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are critical, in the sense that they are expected to mediate…
In this paper we investigate the well-posedness of backward or forward stochastic differential equations whose law is constrained to live in an a priori given (smooth enough) set and which is reflected along the corresponding ''normal''…
The constraint-preserving approach, which aim is to provide consistent boundary conditions for Numerical Relativity simulations, is discussed in parallel with other recent developments. The case of the Z4 system is considered, and…
We show the well-posed variational principle in constraint systems. In a naive procedure of the variational principle with constraints, the proper number of boundary conditions does not match with that of physical degrees of freedom…
We present a novel method to compute componentwise transient bounds, ultimate bounds, and invariant regions for a class of switching continuous-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The…
In this paper, a state feedback control design with min/max operational limiting constraints is developed for multi-input-multi-output linear time invariant systems. Specifically, servo-tracking control problems with input and output…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of…