Related papers: Dynamical Systems with a Cyclic Sign Variation Dim…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
Complete Lyapunov functions for a dynamical system, given by an autonomous ordinary differential equation, are scalar-valued functions that are strictly decreasing along orbits outside the chain-recurrent set. In this paper we show that we…
This paper deals with the stability analysis problem of discrete-time switched linear systems with ranged dwell time. A novel concept called L-switching-cycle is proposed, which contains sequences of multiple activation cycles satisfying…
The principle of least action is one of the most fundamental physical principle. It says that among all possible motions connecting two points in a phase space, the system will exhibit those motions which extremise an action functional.…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
Motivated by reduction of computational complexity, this work develops sign-error adaptive filtering algorithms for estimating time-varying system parameters. Different from the previous work on sign-error algorithms, the parameters are…
Markov decision process over vector addition system with states (VASS MDP) is a finite state model combining non-deterministic and probabilistic behavior, augmented with non-negative integer counters that can be incremented or decremented…
This work is concerned with the stability properties of linear stochastic differential equations with random (drift and diffusion) coefficient matrices, and the stability of a corresponding random transition matrix (or exponential…
Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
In this paper, we consider the stability of discrete-time linear switched systems with a common non-strict Lyapunov matrix.
The paper describes a novel method for studying the stability of nonautonomous dynamical systems. This method based on the flow and divergence of the vector field with coupling to the method of Lyapunov functions. The necessary and…
We consider bounded extremum seeking controls for time-varying linear systems with uncertain coefficient matrices and measurement uncertainty. Using a new change of variables, Lyapunov functions, and a comparison principle, we provide…
The derivation of the equations of motion for nonholonomic systems remains a central issue in analytical mechanics, primarily due to the tension between the d'Alembert-Lagrange differential principle and integral variational approaches.…
Transition systems are often used to describe the behaviour of software systems. If viewed as a graph then, at their most basic level, vertices correspond to the states of a program and each edge represents a transition between states via…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
We study the evolution of observables of dynamical systems. For linear systems, we show that observables satisfy a closed differential equation whose minimal order is determined by the dynamical system and observation operator. This yields…
This paper studies the equivalence between differentiable and non-differentiable dynamics in Rn. Filippov's theory of discontinuous differential equations allows us to find flow solutions of dynamical systems whose vector fields undergo…
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…
In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive Control (MPC) scheme, recently introduced in [2], when restricted to the class of…