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Mathematical Outlines
Published in Federico Milano, Ioannis Dassios, Muyang Liu, Georgios Tzounas, Eigenvalue Problems in Power Systems, 2020
Federico Milano, Ioannis Dassios, Muyang Liu, Georgios Tzounas
A matrix pencil is a polynomial matrix – possibly of infinite order –. Matrix pencil theory has been used many times in studying linear dynamical systems such as: linear systems of differential equations, see [24, 34, 37], linear discrete time systems, see [35], and linear systems of fractional operators, see [38]. Before we define the matrix pencil let us understand why the need to introduce this concept. We consider the following system of differential equations: Ex.(t)=Ax(t),
A Review of Parametric High-Resolution Methods
Published in Yingbo Hua, Alex B. Gershman, Qi Cheng, High-Resolution and Robust Signal Processing, 2017
A matrix pencil is defined as the matrix Y2 — zY1 for an arbitrary matrix pair [Y2, Y1] of the same dimensions. The techniques to be discussed in this subsection yield the signal poles zi, i = 1,2, ..., I, as the rank reducing numbers of a matrix pencil constructed from data directly or indirectly. The accuracy of the matrix pencil methods is about the same as the SVD linear prediction based techniques. But the computational complexity of the matrix pencil methods is generally lower than the SVD linear prediction methods.
Smart Antennas for Contemporary Wireless Communication Systems: Concepts, Challenges, and Performance
Published in Devendra Kumar Sharma, Rohit Sharma, Bhadra Pokharel, Vinod Kumar, Raghvendra Kumar, Advances in Antenna, Signal Processing, and Microelectronics Engineering, 2021
Garima Srivastava, Neeta Singh, Sachin Kumar
Matrix pencil method. This technique is generally used for real-time systems. It is much efficient than the other two techniques. In this method, the radiator behaves like a sensor that selects the spatial bandwidth of the array [17]. The DOA is calculated from the peaks of the spectrum.
Discounted cost linear quadratic Gaussian control for descriptor systems
Published in International Journal of Control, 2022
Hermann Mena, Lena-Maria Pfurtscheller, Matthias Voigt
We consider the stochastic system with additive noise where the matrices are such that is not the zero polynomial. A matrix pencil fulfilling this condition is called regular. Let , and w be an -dimensional Wiener process. The stochastic process is called input and generalised state. We assume that the initial value is a random variable that is independent of w. We denote the set of such systems (1) by and we write . Throughout this paper, the following notation is used: is a complete probability space with sample space Ω, σ-algebra , filtration and probability measure . We denote by the expectation operator with respect to the probability measure .
Frequency domain integrals for stability preservation in Galerkin-type projection-based model order reduction
Published in International Journal of Control, 2021
We consider linear time-invariant systems in the form with state/inner variables , inputs and outputs . The system includes constant matrices , and . If the mass matrix E is non-singular, then system (1) consists of ordinary differential equations (ODEs). If the mass matrix E is singular, then differential-algebraic equations (DAEs) are given. The pair is called a matrix pencil. We assume that the matrix pencil is regular, i.e. for some . ODEs always yield a regular matrix pencil. We add predetermined initial values , which are assumed to be consistent in the case of DAEs.
Secure state estimation for cyber-physical systems under sparse data injection attacks: a switched counteraction approach
Published in International Journal of Control, 2022
Note that and , then (4) is with the following form when where and . Then the rank of modified sparse matrix pencil satisfies The rest of the proof can be carried out along the same line as that of Proposition 3.1.