4 research outputs found
Stability analysis of time-delay systems in the parametric space
This paper presents a novel method for stability analysis of a wide class of
linear, time-delay systems (TDS), including retarded non-neutral ones, as well
as those incorporating incommensurate and distributed delays. The proposed
method is based on frequency domain analysis and the application of Rouche's
theorem. Given a parametrized TDS, and some parametric point for which the
number of unstable poles is known, the proposed method is capable of
identifying the maximum surrounding region in the parametric space for which
the number of unstable poles remains invariant. First, a procedure for
investigating stability along a line is developed. Then, the results are
extended by the application of Holder's inequality to investigating stability
within a region. Contrary to existing approaches, the proposed method is
uniformly applicable to parameters of different types (delays, distributed
delay limits, time constants, etc.). Efficacy of the proposed method is
demonstrated using illustrative examples.Comment: 11 pages, 5 figures, submitted to Automatic
Adaptive Parameter Estimation in LTI Systems
An adaptive algorithm solving the on-line parameter estimation problem for a broad class of linear systems is proposed.
The approach can be applied to systems with delay, distributedparameter systems, fractional-order systems, and others that are
stable or stabilized by linear feedback. The proposed scheme can be applied to simultaneously track sufficiently slow changes in
process gains, delays, time constants, diffusivity, and other parameters. The proposed method is gradient-based, and it yields a
relatively efficient numerical implementation. Convergence and robustness of the algorithm are investigated through Lyapunov analysis, yielding explicit convergence conditions that generalize the
well-known “persistence of excitation” and identifiability requirements arising in conventional adaptive estimation. The method is
illustrated by several examples