Related papers: Stability of hybrid Levy systems
The state of many physical, biological and socio-technical systems evolves by combining smooth local transitions and abrupt resetting events to a set of reference values. The inclusion of the resetting mechanism not only provides the…
Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
We study stability issue of reset and impulsive switched systems. We find time constraints (dwell time and flee time) on switching signals which stabilize a given reset switched system. For a given collection of matrices, we find an…
Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…
We explore a stochastic model that enables capturing external influences in two specific ways. The model allows for the expression of uncertainty in the parametrisation of the stochastic dynamics and incorporates patterns to account for…
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…
Delays are ubiquitous in modern hybrid systems, which exhibit both continuous and discrete dynamical behaviors. Induced by signal transmission, conversion, the nature of plants, and so on, delays may appear either in the continuous…
In this paper, we investigate asymptotic stability of linear time-varying systems with (sub-) stochastic system matrices. Motivated by distributed dynamic fusion over networks of mobile agents, we impose some mild regularity conditions on…
We address the stabilization of both classical and quantum systems modeled by jump-diffusion stochastic differential equations using a novel hysteresis switching strategy. Unlike traditional methods that depend on global Lyapunov functions…
This work addresses the problem of optimally steering the state covariance of a linear stochastic system from an initial to a target, subject to hybrid transitions. The nonlinear and discontinuous jump dynamics complicate the control design…
This paper studies the problem of online stabilization of an unknown discrete-time linear time-varying (LTV) system under bounded non-stochastic (potentially adversarial) disturbances. We propose a novel control algorithm based on convex…
This paper investigates the finite time stabilization problem for a class of nonlinear systems with unknown control directions and unstructured uncertainties. The unstructured uncertainties indicate that not only the parameters but also the…
We analyze confining mechanisms for L\'evy flights evolving under an influence of external potentials. Given a stationary probability density function (pdf), we address the reverse engineering problem: design a jump-type stochastic process…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
We study networked control of non-linear systems where system states and tentative plant input sequences are transmitted over unreliable communication channels. The sequences are calculated recursively by using a pre-designed nominally…
Stochastic Spatio-Temporal processes are prevalent across domains ranging from modeling of plasma to the turbulence in fluids to the wave function of quantum systems. This letter studies a measure-theoretic description of such systems by…
This paper is concerned with the stability analysis of continuous-time switched systems with a random switching signal. The switching signal manifests its characteristics with that the dwell time in each subsystem consists of a fixed part…
It is known that the implied volatility skew of FX options demonstrates a stochastic behavior which is called stochastic skew. In this paper we create stochastic skew by assuming the spot/instantaneous variance correlation to be stochastic.…
We combine geometric data analysis and stochastic modeling to describe the collective dynamics of complex systems. As an example we apply this approach to financial data and focus on the non-stationarity of the market correlation structure.…