Related papers: A Robust Stability Condition for Subhomogeneous Co…
We extend the setup in our previous paper to deal with the case in which more than one steady state may exist in feedback configurations. This provides a foundation for the analysis of multi-stability and hysteresis behaviour in high…
The sequential compactness afforded hybrid systems under mild regularity constraints guarantee outer/upper semicontinuous dependence of solutions on initial conditions and perturbations. For reachable sets of hybrid systems, this property…
We analyze a classification of two main families of controllers that are of interest when the feedback loop is subject to switching propagation delays due to routing via a wireless multi-hop communication network. We show that we can cast…
It is well-known that wave-type equations with memory, under appropriate assumptions on the memory kernel, are uniformly exponentially stable. On the other hand, time delay effects may destroy this behavior. Here, we consider the…
We study the asymptotic behavior of the solutions of the time-delayed higher-order dispersive nonlinear differential equation \begin{equation*} u_t(x,t)+Au(x,t) +\lambda_0(x) u(x,t)+\lambda(x) u(x,t-\tau )=0 \end{equation*} where…
This paper presents finite-time and fixed-time stabilization results for inhomogeneous abstract evolution problems, extending existing theories. We prove well-posedness for strong and weak solutions, and estimate upper bounds for settling…
Using the model of a generalized Van der Pol oscillator in the regime of subcritical Hopf bifurcation we investigate the influence of time delay on noise-induced oscillations. It is shown that for appropriate choices of time delay either…
This thesis addresses the question of stability of systems defined by differential equations which contain nonlinearity and delay. In particular, we analyze the stability of a well-known delayed nonlinear implementation of a certain…
This paper studies robustness of MIMO control systems with parametric uncertainties, and establishes a lower dimensional robust stability criterion. For control systems with interval transfer matrices, we identify the minimal testing set…
We suggest a spatially local feedback mechanism for stabilizing periodic orbits in spatially extended systems. Our method, which is based on a comparison between present and past states of the system, does not require the external…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
In this paper, we investigate delayed linear difference systems and establish several fundamental results. We first provide a Kalman-type rank condition tailored for delayed linear difference systems. Furthermore, we construct the discrete…
In this paper, the feasibility of recently developed higher order delayed sliding mode controllers is addressed. With this aim the robustness against the measurement noise and mismatched perturbations for the systems governed by such…
The current series of papers is concerned with stochastic stability of monotone dynamical systems by identifying the basic dynamical units that can survive in the presence of noise interference. In the first of the series, for the…
Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
Solutions to the interval observation problem for delayed impulsive and switched systems with $L_1$-performance are provided. The approach is based on first obtaining stability and $L_1/\ell_1$-to-$L_1/\ell_1$ performance analysis…
This paper presents a mathematical approach for improving the performance of a control system by modifying the time delay at certain operating conditions. This approach converts a continuous time loop into a discrete time loop. The formula…
In this paper, we consider the asymptotic stability for a system of linear delay differential equations. By analysing of the characteristic equation in detail, we have established the necessary and sufficient condition for the asymptotic…
This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. System-theoretic results are provided for both classes of…