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For efficiently solving large dense complex linear systems with multiple right-hand sides that arise in monostatic radar cross section (RCS) calculation, a spectral multiresolution method combined with the multilevel fast multipole algorithm (MLFMA) is developed and used in the context of the generalized minimal residual iterative method (GMRES). In this scheme, the MLFMA is used to speed up the matrix...
It is well-known that the stability of linear periodic (LP) systems can be assessed using Floquet Characteristic Exponents (FCE). In this paper, a new method is presented for evaluating FCE for nth-order scalar periodic linear systems based on a recently developed unified eigenvalue theory for linear time-varying (LTV) Systems [1]. The new theory allows FCEs to be evaluated from the DC term of the...
In this paper, two new spectra?? canonical relizations are developed for the class of time-varying Scalar Linear Dynamical Systems (SLDS) of the form: y(n)+??n(t)y(n-1)+...+??2(t)??+ ??1(t)y=??(t)u(n)+??n(t)u(n-1)+...+ ??2(t)u??+??1(t)u, and the class of completely controllable time-varying Vector Linear Dynamical Systems (VLDS) of the form: x??=A(t)x+b(t)u, y=C(t)x+d(t)u, where A(t), b(t), C(t) and...
The controlled pointing of an Earth-orbiting astronomical telescope in the presence of time-dependent gravity-gradient torques is studied using recent techniques for the analysis and synthesis of time-varying linear scalar dynamical systems. We present results which show that effective adaptive control of unstable motions due to gravity gradient torques can be accomplished, resulting in high pointing...
In a series of recent papers [11], [12], the new notions of ED-eigenvalues, D-spectra, D-characteristic equation, and D-similarity transformations were introduced for (time-varying) Vector Linear Dynamical Systems (VLDS) of the form ??= A(t)x and Scalar LDS (SLDS) of the form y(n) + ??nk=1 ??k(t)y(k-1)=0. The present paper establishes several fundamental features of D-similarity classes of (time-varying)...
Let A(t) be a real-valued matrix function on [0, + ??]. A (time-varying) Linear Dynamical Systems (LDS) of the form x=A(t)x is said to be well-defined if A(t) is Lebesgue integrable on every finite subinterval of [0, + ??], and is called proper if A(t)=f(t,G) for some constant generating matrix G and scalar primitive function f(t, ??) (see [13], [15]). According to a recent result obtained in [17],...
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