Analyticity Conditions of Characteristic and Disturbing Quasipolynomials of Hybrid Dynamical Systems

Analysis of application of entropy methods of vibration diagnostic signal processing to assess technical condition of pipelines

“…Discrete Wavelet Transform (DWT) is an implementation of a wavelet transform using a discrete set of wavelet scales and translations that obey certain specific rules [11]. DWT decomposes the signal into a mutually orthogonal set of wavelets, it is the main difference from the continuous wavelet transform (CWT).…”

“…For discrete-time sequences, you can also use this transform, with the restriction that the smallest wavelet translations should be equal to the data sampling. This is sometimes called Discrete-Time Continuous Wavelet Transform (DT-CWT) and is the most commonly used method for calculating CWT in practice [11].…”

Hybrid Automation Extended Model

“…are matrices whose elements are perturbing quasi-polynomials of HDS. In [10] the conditions for the analyticity of the functions B u (λ) and C u (λ), as well as the characteristic and perturbing quasi-polynomials D(λ) and Q(λ) are formulated and proved in the domain |λ| ≫ 1, Re λ > − |λ| sin α, 0 < α < π/2 (conditions with respect to the functions C 2 (λ) and C 3 (λ), as well as perturbing quasi-polynomials Q 1 (λ), Q 2 (λ) and Q 3 (λ) can be formulated and proved similarly). In particular, with sufficiently general assumptions, this is true for a number of typical mathematical models of control objects with distributed parameters (heat conduction and diffusion processes, damping and supporting layers of a viscous incompressible fluid, the dynamics of an elastic medium with a small but finite energy dissipation).…”

“…The generalized degree n ∈ R of the characteristic quasi-polynomial D(λ) is determined from the condition [9,10]…”

“…The numerical solution of auxiliary linear boundary value problems (25) with |λ| < R, R ≫ 1, Re λ > −ε, 0 < ε ≪ 1 is performed on the basis of the Galerkin projection method [10]. In the considered domain, the absence of singularities of functions B u (λ), C u (λ), C 2 (λ), C 3 (λ) and, consequently, of the characteristic and perturbing quasipolynomials D(λ), Q(λ), Q 1 (λ), Q 2 (λ), Q 3 (λ) is verified numerically on the basis of principle of argument.…”