Related papers: Bounding the State Covariance Matrix for a Randoml…
We look into the fluctuations caused by disturbances in power systems. In the linearized system of the power systems, the disturbance is modeled by a Brownian motion process, and the fluctuations are described by the covariance matrix of…
In this paper, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state…
This contribution proposes a recursive, computationally efficient, ready-to-use, online method for the ellipsoidal state characterization for linear discrete-time models with additive unknown disturbances vectors (bounded by known possibly…
We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this…
A model is proposed that describes the evolution of a mixed state of a quantum system for which gain and loss of energy or amplitude are present. Properties of the model are worked out in detail. In particular, invariant subspaces of the…
The statistical behavior of a nonlinear system described by a mapping with phase rotation is studied. We use the Kolmogorov-Chapman equations for the multi-time probability distribution functions for investigation of dynamics under the…
This paper concerns about the large time behavior of acoustic wave motion driven by a random force acting through the boundary. We begin with an abstract result showing the interconnection between the regularity of Markov semigroup…
This work addresses the finite-horizon robust covariance control problem for discrete-time, partially observable, linear system affected by random zero mean noise and deterministic but unknown disturbances restricted to lie in what is…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
This paper introduces a linear state-space model with time-varying dynamics. The time dependency is obtained by forming the state dynamics matrix as a time-varying linear combination of a set of matrices. The time dependency of the weights…
In this paper, we study a linear control system with a given state feedback law. The system is influenced by rapid random sampling occurring at frequency $\frac 1n, n \in \mathbb N$, as well as by white noise of small intensity $\varepsilon…
In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce…
This paper considers the state transition of the stochastic Morris-Lecar neuronal model driven by symmetric $\alpha$-stable L\'evy noise. The considered system is bistable: a stable fixed point (resting state) and a stable limit cycle…
This paper studies the set of terminal state covariances that are reachable over a finite time horizon from a given initial state covariance for a linear stochastic system with additive noise. For discrete-time systems, a complete…
This work focuses on modeling of time-varying covariance matrices using the state covariance of linear stochastic systems. Following concepts from optimal mass transport and the Schr\"odinger bridge problem (SBP), we investigate several…
This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for…
Light scattering from resonantly or nearly resonantly excited systems, known as resonance fluorescence, has been gaining importance as a versatile tool for investigating quantum states of matter and readout of quantum information, recently…
Fluctuation properties of the Langevin equation including a multiplicative, power-law noise and a quadratic potential are discussed. The noise has the Levy stable distribution. If this distribution is truncated, the covariance can be…
Coupling dynamics of the states of the nodes of a network to the dynamics of the network topology leads to generic absorbing and fragmentation transitions. The coevolving voter model is a typical system that exhibits such transitions at…
Gaussian states are the backbone of quantum information protocols with continuous variable systems, whose power relies fundamentally on the entanglement between the different modes. In the case of global pure states, knowledge of the…