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The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction. To avoid this problem we add to the system, at the delayed equation, a Kelvin-Voigt damping. In this note we…
This paper deals with the problem of covariance stabilization for a class of linear stochastic discrete-time systems in the Stochastic Model Predictive Control (SMPC) framework. The considered systems are affected by independent and…
The dynamical behavior of switched affine systems is known to be more intricate than that of the well-studied switched linear systems, essentially due to the existence of distinct equilibrium points for each subsystem. First, under…
Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…
We describe a situation where an unstable equilibrium in a $3 \times 3$ system of linear differential equations may be stabilized by introducing a delayed response, i.e. converting to a system of delayed differential equations. This…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
Using the white noise setting, in particular the Wick product, the Hermite transform, and the Kondratiev space, we present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
Incremental stability properties are considered for certain systems of forced, nonlinear differential equations with a particular positivity structure. An incremental stability estimate is derived for pairs of input/state/output…
A previously published algorithm for trajectory tracking control of tethered wings, i.e. kites, is updated in light of recent experimental evidence. The algorithm is, furthermore, analyzed in the framework of delay differential equations.…
Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
The problem of estimating the initial state of 1-D wave equations with globally Lipschitz nonlinearities from boundary measurements on a finite interval was solved recently by using the sequence of forward and backward observers, and…
A wide variety of integral inequalities (IIs) have been developed and studied for the stability analysis of distributed parameter systems using the Lyapunov functional approach. However, no unified mathematical framework has been proposed…
A static non-linear homogeneous feedback for a fixed-time stabilization of a linear time-invariant (LTI) system is designed in such a way that the settling time is assigned exactly to a prescribed constant for all nonzero initial…
We analyse the problem of stability of a continuous time linear switching system (LSS) versus the stability of its Euler discretization. It is well-known that the existence of a positive {\tau} for which the corresponding discrete time…
The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
A nonlinear stochastic differential equation with the order of nonlinearity higher than one, with several discrete and distributed delays and time varying coefficients is considered. It is shown that the sufficient conditions for…
A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…