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Imprecise continuous-time Markov chains are a robust type of continuous-time Markov chains that allow for partially specified time-dependent parameters. Computing inferences for them requires the solution of a non-linear differential…
In this paper, we characterize the stability of matrix-valued Markovian chains by periodic data.
In most real cases transition probabilities between operational modes of Markov jump linear systems cannot be computed exactly and are time-varying. We take into account this aspect by considering Markov jump linear systems where the…
The Markov-Bernstein type inequalities between the norms of functions and of their derivatives are analysed for complex exponential polynomials. We establish a relation between the sharp constants in those inequalities and the stability…
This paper presents a Bayesian method for identification of jump Markov linear system parameters. A primary motivation is to provide accurate quantification of parameter uncertainty without relying on asymptotic in data-length arguments. To…
The estimation of absorption time distributions of Markov jump processes is an important task in various branches of statistics and applied probability. While the time-homogeneous case is classic, the time-inhomogeneous case has recently…
This paper develops a new approach to the estimation of the degree of boundedness or stability of multidimensional nonlinear systems with time-dependent nonperiodic coefficients-an essential task in various engineering and natural science…
In this work, we propose the design and analysis of a novel continuous robust controller for a class of multi--input multi--output (MIMO) nonlinear uncertain systems. The systems under consideration contains unstructured uncertainties in…
Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models…
In this note, we provide a unified framework for the mean square stability of stochastic jump linear systems via optimal transport. The Wasserstein metric known as an optimal transport, that assesses the distance between probability density…
This paper proposes a novel Gronwall inequality-based method for transient stability assessment for power systems. The challenges of applying such methods to power systems are how to construct the differential inequality and how to treat…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
In this paper, we solve the chance-constrained covariance steering problem for discrete-time Markov Jump Linear Systems (MJLS) using a convex optimization framework. We derive the analytical expressions for the mean and covariance…
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…
Markov chain Monte Carlo methods are central in computational statistics, and typically rely on detailed balance to ensure invariance with respect to a target distribution. Although straightforward to construct by Metropolization, this can…
We study the problem of system identification for stochastic continuous-time dynamics, based on a single finite-length state trajectory. We present a method for estimating the possibly unstable open-loop matrix by employing properly…
In this paper exponential stability of nonlinear fractional order stochastic system with Poisson jumps is studied in finite dimensional space. Existence and uniqueness of solution, stability and exponential stability results are established…
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…
Identification of the parameters of stable linear dynamical systems is a well-studied problem in the literature, both in the low and high-dimensional settings. However, there are hardly any results for the unstable case, especially…
Robust stability problem of integral delay systems with uncertain kernel matrix functions is addressed in this paper. On the basis of characteristic equation and the argument principle, an algorithm is generated which is shown to outperform…