Related papers: Left invertibility of discrete-time output-quantiz…
This brief note concerns the invertibility of certain alternant matrices. In particular those that consisting of polynomials and products of polynomials and logarithms are shown to be invertible under appropriate conditions on the degrees…
For linear control systems in discrete time controllability properties are characterized. In particular, a unique control set with nonvoid interior exists and it is bounded in the hyperbolic case. Then a formula for the invariance pressure…
This paper introduces a novel technique to decide the satisfiability of formulae written in the language of Linear Temporal Logic with Both future and past operators and atomic formulae belonging to constraint system D (CLTLB(D) for short).…
We here show that the family of finite-dimensional, discrete-time, passive, linear time-invariant systems can be characterized through the structure of maximal, matrix-convex set, closed under multiplication among its elements. Moreover,…
The purpose of this paper is to investigate system identification for single-input-single-output general (active or passive) quantum linear systems. For a given input we address the following questions: (1) Which parameters can be…
The concept of divisibility of dynamical maps is used to introduce an analogous concept for quantum channels by analyzing the \textit{simulability} of channels by means of dynamical maps. In particular, this is addressed for Lindblad…
In this paper we generalize the involutive methods and algorithms devised for polynomial ideals to differential ones generated by a finite set of linear differential polynomials in the differential polynomial ring over a zero characteristic…
Solving linear systems and computing eigenvalues are two fundamental problems in linear algebra. For solving linear systems, many efficient quantum algorithms have been discovered. For computing eigenvalues, currently, we have efficient…
We show that the flatness of a nonlinear discrete-time system can be checked by computing a unique sequence of involutive distributions. The well-known test for static feedback linearizability is included as a special case. Since the…
Termination analysis of linear loops plays a key r\^{o}le in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination…
We show that the quantized free relativistic point particle can be understood as a string in a Clifford space which generates the space-time coordinates through its inner product. The generating algebra is preserved by a unitary symmetry…
Designing quantum processors is a complex task that demands advanced verification methods to ensure their correct functionality. However, traditional methods of comprehensively verifying quantum devices, such as quantum process tomography,…
In this paper I investigate the usability of the characteristic functions for the description of the dynamics of open quantum systems focussing on non-Lindblad-type master equations. I consider, as an example, a non-Markovian generalized…
We study invertibility of matrices of the form $D+R$ where $D$ is an arbitrary symmetric deterministic matrix, and $R$ is a symmetric random matrix whose independent entries have continuous distributions with bounded densities. We show that…
A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to…
Finding the Lie-algebraic closure of a handful of matrices has important applications in quantum computing and quantum control. For most realistic cases, the closure cannot be determined analytically, necessitating an explicit numerical…
For a closed-loop control system with a digital channel between the sensor and the controller, the notion of invariance entropy quantifies the smallest average rate of information above which a given compact subset of the state space can be…
This paper is concerned with computations of a few smaller eigenvalues (in absolute value) of a large extremely ill-conditioned matrix. It is shown that smaller eigenvalues can be accurately computed for a diagonally dominant matrix or a…
Flatness of discrete-time systems can be characterized by two simple properties. There exists a map, a submersion, from the flat coordinates and their forward shifts to the state and the input of the discrete-time system, such that the…
We present a practical Newton-based method for computing left eigenvalues of quaternion matrices. It uses only standard real/complex linear-algebra kernels via embeddings and applies to matrices of any size. Extensive tests on literature…