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Space Time Block Coded MIMO Systems
Published in Brijesh Kumbhani, Rakhesh Singh Kshetrimayum, MIMO Wireless Communications over Generalized Fading Channels, 2017
Brijesh Kumbhani, Rakhesh Singh Kshetrimayum
‖(X2-X1)H‖F. This Frobenius norm was evaluated in the previous section using the relation between trace of a matrix and its Frobenius norm. Now, we will follow an alternate way to obtain the required Frobenius norm. It still uses the relation between trace of a matrix and its Frobenius norm. But, now we use the fact that
Localization
Published in Prabhakar S. Naidu, Distributed Sensor Arrays Localization, 2017
where ʌ is the error matrix in the system matrix, (A), and ‖⋅‖F stands for the Frobenius norm of a matrix. The Frobenius norm is defined as a square root of the sum of the mod square of all matrix elements. We minimally perturb the system matrix A and data vector b while the constraint in Equation 4.75 is satisfied. Let us express this constraint in a slightly different form,
Linear Systems
Published in Jeffery J. Leader, Numerical Analysis and Scientific Computation, 2022
defines a matrix norm, called the Frobenius norm. It can be shown that ‖A‖F=tr(ATA)
Robust nonlinear state estimation for a class of infinite-dimensional systems using reduced-order models
Published in International Journal of Control, 2021
Mouhacine Benosman, Jeff Borggaard
For a vector , its transpose is denoted by , for a matrix , the transpose is denoted by . The Euclidean vector norm for is denoted by so that . The Frobenius norm of a matrix , with elements , is defined as . The Kronecker delta function is defined as: and . We shall abbreviate the time derivative by , and consider the following Hilbert space . We define the inner product and the associated norm on as , for , and . A function is in if for each , , and . We will use the standard notation from distributed parameter control theory and drop the ‘·’ when it is understood, e.g. . A pseudo-inverse of an operator on will be denoted as , and its adjoint operator on is denoted by . In the sequel when we discuss the boundedness of a solution for an impulsive dynamical system, we mean uniform boundedness as defined in Haddad, Chellaboind, and Nersesov (2006, p. 67, Definition 2.12). Finally, an impulsive dynamical system is said to be well-posed, if it has well-defined distinct resetting times, admits a unique solution over a finite forward time interval, and does not exhibit any Zeno solutions, i.e. does not have an infinite number of resettings in the system over any finite time interval (Haddad et al., 2006).