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This work defines two classes of processes, that we term {\it tempered fractional multistable motion} and {\it tempered multifractional stable motion}. They are extensions of fractional multistable motion and multifractional stable motion,…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
The monitoring of event frequencies can be used to recognize behavioral anomalies, to identify trends, and to deduce or discard hypotheses about the underlying system. For example, the performance of a web server may be monitored based on…
We address a class of Markov jump linear systems that are characterized by the underlying Markov process being time-inhomogeneous with a priori unknown transition probabilities. Necessary and sufficient conditions for uniform stochastic…
We provide novel sufficient conditions for stability of nonlinear and time-varying impulsive systems. These conditions generalize, extend, and strengthen many existing results. Different types of input-to-state stability (ISS), as well as…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general…
In this paper, we consider a class of multi-dimensional stochastic delay differential equations with jump reflection. Based on existence and uniqueness of the strong solution to the equation, we prove that the Markov semigroup generated by…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
Stochastic processes that are randomly reset to an initial condition serve as a showcase to investigate non-equilibrium steady states. However, all existing results have been restricted to the special case of memoryless resetting protocols.…
The paper deals with a certain class of random evolutions. We develop a construction that yields an invariant measure for a continuous-time Markov process with random transitions. The approach is based on a particular way of constructing…
We register a random sequence which has the following properties: it has three segments being the homogeneous Markov processes. Each segment has his own one step transition probability law and the length of the segment is unknown and…
In this work, we study finite-time stability of switched and hybrid systems in the presence of unstable modes. We present sufficient conditions in terms of multiple Lyapunov functions for the origin of the system to be finite time stable.…
We propose a computational method for large deviation statistics of time-averaged quantities in general Markov processes. In our proposed method, we repeat a response measurement against external forces, where the forces are determined by…
We study qualitative properties of the set of recurrent points of finitely generated free semigroups of measurable maps. In the case of a single generator the classical Poincare recurrence theorem shows that these properties are closely…
We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with…
Sampling arises simultaneously with input and output delays in networked control systems. When the delay is left uncompensated, the sampling period is generally required to be sufficiently small, the delay sufficiently short, and, for…
Large deviation results are given for a class of perturbed nonhomogeneous Markov chains on finite state space which formally includes some stochastic optimization algorithms. Specifically, let {P_n} be a sequence of transition matrices on a…
Using two simple examples, the continuous-time random walk as well as a two state Markov chain, the relation between generalized anomalous relaxation equations and semi-Markov processes is illustrated. This relation is then used to discuss…
We consider continuous--time Markov kinetics with a finite number of states and a given positive equilibrium distribution P*. For an arbitrary probability distribution $P$ we study the possible right hand sides, dP/dt, of the Kolmogorov…