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We consider a class of continuous-time hybrid dynamical systems that correspond to subgradient flows of a piecewise linear and convex potential function with finitely many pieces, and which include the fluid-level dynamics of the Max-Weight…
In this technical communique we study the maximal robust positively invariant set for state-constrained continuous-time nonlinear systems subjected to a bounded disturbance. Extending results from the theory of barriers, we show that this…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
Sensitive boundary condition dependence (BCD) is reported in a convectively unstable system with noise, where the amplitude of generated oscillatory dynamics in the downstream depends sensitively on the boundary value. This BCD is explained…
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…
We develop a rigorous theory of external influences on finite discrete dynamical systems, going beyond the perturbation paradigm, in that the external influence need not be a small contribution. Indeed, the covariance condition can be…
In this paper, we present a novel framework for quantifying a lower bound on resilience in continuous-time (non)linear systems subject to external disturbances while ensuring satisfaction of signal temporal logic specifications. Unlike…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
A binary fluid mixture in contact with lateral particle reservoirs is considered. By imposing different particle concentrations in these reservoirs, the system can be maintained under controlled non-equilibrium conditions. Previous…
This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models…
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…
The paper investigates dynamical systems for which the derivative of some positive-definite function along the solutions of this system depends on so-called density function. In turn, such dynamical systems are called density systems. The…
The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional)…
We investigate the stabilizability of discrete-time linear switched systems, when the sole control action of the controller is the switching signal, and when the controller has access to the state of the system in real time. Despite their…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $(X,T)$ given by a compact metric space $X$ and a continuous…
The limiting slow dynamics of slow-fast, piecewise-linear, continuous systems of ODEs occurs on critical manifolds that are piecewise-linear. At points of non-differentiability, such manifolds are not normally hyperbolic and so the…
Control systems should enforce a desired property for both expected modeled situations as well as unexpected unmodeled environmental situations. Existing methods focus on designing controllers to enforce the desired property only when the…
A novel method for control of dynamical systems, proposed in the paper, ensures an output signal belonging to the given set at any time. The method is based on a special change of coordinates such that the initial problem with given…
Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that…