Related papers: Commutativity and Commutative Pairs of Some Differ…
After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear…
Commutativity of subsystems in cascade connected forms to form larger systems gets worthy to improve noise disturbance properties, stability, robustness and many other properties in system design. In this paper, another benefit of…
Although the explicit commutativitiy conditions for second-order linear time-varying systems have been appeared in some literature, these are all for initially relaxed systems. This paper presents explicit necessary and sufficient…
Decomposition is a common tool for synthesis of many physical systems. It is also used for analyzing large scale systems which then known as tearing and reconstruction. On the other hand, commutativity of cascade connected systems have…
After reviewing commutativity of second-order linear time-varying analog systems, the inverse commutativity conditions are derived for these systems by considering non-zero initial conditions. On the base of these conditions, the…
In this contribution, the transitivity property of commutative first-order linear time-varying systems is investigated with and without initial conditions. It is proven that transitivity property of first-order systems holds with and…
After introducing commutativity concept and summarizing the relevant literature, this work is focused on the commutativity of feedback conjugates. It is already known that a linear time-varying differential system describing a single…
The completeness of the group classification of systems of two linear second-order ordinary differential equations with constant coefficients is delineated in the paper. The new cases extend what has been done in the literature. These cases…
Results of research of possibility of transformation of a difference equation into a system of the first-order difference equation are presented. In contrast to the method used previously, an unknown grid function is split into two new…
This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…
The linearization of complex ordinary differential equations is studied by extending Lie's criteria for linearizability to complex functions of complex variables. It is shown that the linearization of complex ordinary differential equations…
Effective matrix methods for solving standard linear algebra problems in a commutative domains are discussed. Two of them are new. There are a methods for computing adjoined matrices and solving system of linear equations in a commutative…
The Lie linearizability criteria are extended to complex functions for complex ordinary differential equations. The linearizability of complex ordinary differential equations is used to study the linearizability of corresponding systems of…
Extensive monitoring systems generate data that is usually compressed for network transmission. This compressed data might then be processed in the cloud for tasks such as anomaly detection. However, compression can potentially impair the…
The goal of demonstrating a quantum advantage with currently available experimental systems is of utmost importance in quantum information science. While this remains elusive for quantum computation, the field of communication complexity…
A system of inhomogeneous second-order difference equations with linear parts given by noncommutative matrix coefficients are considered. Closed form of its solution is derived by means of newly defined delayed matrix sine/cosine using the…
We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations…
A formal series in noncommuting variables $\Sigma$ over the rationals is a mapping $\Sigma^* \to \mathbb Q$. We say that a series is commutative if the value in the output does not depend on the order of the symbols in the input. The…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
Human sociality depends upon the benefits of mutual aid and extensive communication. However mutual aid is made difficult by the problems of coordinating diverse norms and preferences, and communication is harried by substantial ambiguity…