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The paper presents realization theory of discrete-time linear switched systems. A discrete-time linear switched system is a hybrid system, such that the continuous sub-system associated with each discrete state is linear. In this paper we…
The purpose of this paper is to present a network realization theory for a class of mixed quantum-classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum-classical…
In this paper, we present a complete stochastic realization theory for stochastic jump-linear systems. We present necessary and sufficient conditions for the existence of a realization, along with a characterization of minimality in terms…
The purpose of this paper is to study the realization theory of quantum linear systems. It is shown that for a general quantum linear system its controllability and observability are equivalent and they can be checked by means of a simple…
The paper addresses the realization and identification problem or a subclass of piecewise-affine hybrid systems. The paper provides necessary and sufficient conditions for existence of a realization, a characterization of minimality, and an…
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. We extend its application to the case of formal power series over a field of arbitrary characteristic and illustrate the proposed approach…
It is well-known that the controllability of finite-dimensional nonlinear systems can be established by showing the controllability of the linearized system. However, this classical result does not generalize to infinite-dimensional…
Two possible realizations of the formal neuron are considered as quantum system. The first type complies with classical system. The second type vastly increases the possible problems.
We propose a new method to design adaptation algorithms that guarantee a certain prescribed level of performance and are applicable to systems with nonconvex parameterization. The main idea behind the method is, given the desired…
The purpose of this paper is to show how a class of classical linear stochastic systems can be physically implemented using quantum optical components. Quantum optical systems typically have much higher bandwidth than electronic devices,…
Real world systems of interest often feature interactions between discrete and continuous dynamics. Various hybrid system formalisms have been used to model and analyze this combination of dynamics, ranging from mathematical descriptions,…
The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding…
We study the $\mathcal{L}_p$ induced gain of discrete-time linear switching systems with graph-constrained switching sequences. We first prove that, for stable systems in a minimal realization, for every $p \geq 1$, the $\mathcal{L}_p$-gain…
Linearized models of power systems are often desirable to formulate tractable control and optimization problems that still reflect real-world physics adequately under various operating conditions. In this paper, we propose an approach that…
This paper investigates two issues on identification of switched linear systems: persistence of excitation and numerical algorithms. The main contribution is a much weaker condition on the regressor to be persistently exciting that…
This paper focuses on analyzing and differentiating between lattice linear problems and algorithms. It introduces a new class of algorithms called \textit{(fully) lattice linear algorithms}. A property of these algorithms is that they…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…
Control systems are an integral part of almost every engineering and physical system and thus their accurate analysis is of utmost importance. Traditionally, control systems are analyzed using paper-and-pencil proof and computer simulation…
We consider the solution of complex symmetric shifted linear systems. Such systems arise in large-scale electronic structure simulations and there is a strong need for the fast solution of the systems. With the aim of solving the systems…
Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressions on tuples of matrices. This interpretation extends their…