Determining the stability margin in linear interval parameter electric circuits via a DAE model

Abstract

SUMMARYThis paper addresses the problem of determining the stability margin M s in linear time-invariant electric circuits whose parameters R, L, C, M and controlled source coefficients are allowed to take on fixed but unknown values within corresponding preset intervals. A method for solving the above robust stability problem is suggested. Unlike previous results resorting to the state-space formulation, the new method is based on an appropriate description of the circuit considered using a specific model in semi-state form. The set of differential algebraic equations (DAEs) thus obtained contain the circuit parameters in a linear manner. The latter property permits M s to be determined in an efficient way using the right endpoint of the range related to the real part of the first (closest to the imaginary axis) eigenvalue of a corresponding interval generalized eigenvalue problem. The new method is shown to have polynomial numerical complexity with respect to the size of the generalized eigenvalue problem. Two numerical examples illustrating the new DAE approach are provided.

Necessary and sufficient conditions for regularity of interval parametric matrices

“…Radius of regularity for interval parametric matrices was first defined in [24] under the assumption that r * (A(p), p) < ∞. In several works, e.g., [10], [24], L. Kolev develops and applies a methodology for either finding the regularity radius of an interval parametric matrix or providing bounds for the latter. Beside various other requirements, this methodology also assumes r * (A(p), p) < ∞.…”

“…In view of Definition 3, the regularity radius can be defined equivalently as (10) According to (10)…”

“…Stability of symmetric interval matrices is investigated in [9]. Stability in the general case of parameter dependencies is investigated in [10]. In [11] a sufficient condition for checking strong positive definiteness of an interval parametric matrix employs regularity of the matrix.…”

Hybrid Analysis of Nonlinear Circuits: DAE Models with Indices Zero and One

“…the 1971 paper of Gear [26], the papers of Luenberger in the late 1970s [45,46], the "Pitman books" of Campbell [11,12], the 1981 paper of Newcomb [51], and the 1986 and 1989 special issues of Circuits, Systems, and Signal Processing [41,42]), DAEs have played an increasingly significant role as a modelling and analysis tool within these fields. Recent applications are reported in [2,4,21,35,37,44,47,55,56,57,67,70,71,72].…”