Related papers: Dynamical Systems with a Cyclic Sign Variation Dim…
We consider nonautonomous cyclic systems of delay differential equations with variable delay. Under suitable feedback assumptions, we define an (integer valued) Lyapunov functional related to the number of sign changes of the coordinate…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
A time-varying nonlinear dynamical system is called a totally positive differential system (TPDS) if its Jacobian admits a special sign pattern: it is tri-diagonal with positive entries on the super- and sub-diagonals. If the vector field…
A linear dynamical system is called $k$-positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to the important class of positive linear systems. Since stable positive linear…
We consider $k$-positive linear systems, that is, systems that map the set of vectors with up to $k-1$ sign variations to itself. For $k=1$, this reduces to positive linear systems. It is well-known that stable positive linear time…
This paper addresses the stability problem for discrete-time switched systems under autonomous switching. Each mode of the switched system is modeled as a Linear Parameter Varying (LPV) system, the time-varying parameters can vary…
The concept of dissipativity plays a crucial role in the analysis of control systems. Dissipative energy functionals, also known as Hamiltonians, storage functions, or Lyapunov functions, depending on the setting, are extremely valuable to…
A continuous adaptive control design is developed for nonlinear dynamical systems with linearly parameterizable uncertainty involving time-varying uncertain parameters. The key feature of this design is a robust integral of the sign of the…
This paper is concerned with stability analysis of nonlinear time-varying systems by using Lyapunov function based approach. The classical Lyapunov stability theorems are generalized in the sense that the time-derivative of the Lyapunov…
A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system…
A matrix is called totally nonnegative (TN) if all its minors are nonnegative, and totally positive (TP) if all its minors are positive. Multiplying a vector by a TN matrix does not increase the number of sign variations in the vector. In a…
We define variational properties for dynamical systems with subexponential complexity, and study these properties in certain specific examples. By computing the value of slow entropy directly, we show that some subshifts are not…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
This paper deals with the robust stability analysis of linear systems, subject to time-varying parameters. The Parameter Dependent Lyapunov Function are considered, assuming that the temporal derivative of the parameters are bounded. Some…
Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…
Switched linear hyperbolic partial differential equations are considered in this paper. They model infinite dimensional systems of conservation laws and balance laws, which are potentially affected by a distributed source or sink term. The…
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
Starting from a finite family of continuously differentiable positive definite functions, we study conditions under which a function obtained by max-min combinations is a Lyapunov function, establishing stability for two kinds of nonlinear…
New necessary and sufficient conditions are proposed for the stability investigation of dynamical systems using the flow and the divergence of the phase vector velocity. The obtained conditions generalize the well-known results of V.P.…
We prove vector-valued almost sure invariance principle (VASIP) for nonstationary dynamical systems, under assumptions of correlation decay and variance growth. Applications include VASIP for non-stationary (non)uniformly expanding…