V.Y. Glizer. Stabilizability and Detectability of Singularly Perturbed Linear Time-Invariant Systems with Delays. J. Dynam. Control Systems 5 (1999), no. 2, 153--172.
A singularly perturbed linear time-invariant system with delays in state and control variables is considered. Connection between properties of open-loop stabilizability (detectability) of the reduced-order and boundary-layer systems, associated with the original system, and such properties of the original system itself are analyzed.
G.R. Goodson. A Survey of Recent Results in the Spectral Theory of Ergodic Dynamical Systems. J. Dynam. Control Systems 5 (1999), no. 2, 173--226.
The purpose of this paper is to survey recent results in the spectral theory of ergodic dynamical systems. In addition we prove some known results using new methods and mention some new results, including the recent solution to Rokhlin's problem concerning ergodic transformations having a homogeneous spectrum of multiplicity two. We emphasize applications of ideas arising from the theory of joinings and Markov intertwinings.
V.A. Dobrynskii. Critical Sets and Properties of Endomorphisms Built by Coupling of Two Identical Quadratic Mappings . J. Dynam. Control Systems 5 (1999), no. 2, 227--254.
In this paper, it is shown that there are parameter values such that endomorphisms built by coupling of two identical 1-dimensional quadratic mappings (a) have two kinds of trapping regions in the phase space: a large simply-connected domain inside of which there is a smaller trapping subregion consisting of two disjoint domains; (b) restrictions of the main diagonal $y=x$ of their nonwandering sets are invariant subsets, which may not belong to attractors of the given endomorphisms, but in any way, can be nonisolated in their nonwandering sets. Numerical investigation results represented in the Appendix display the existence of a couple of bifurcation cascades and this leads to a couple of nontrivial symmetrically disposed chaotic strange attractors each of which consists of four disjoint simply connected regions. As parameters vary, these attractors merge into the one consisting at first of two and then of one such region as mentioned above.
K.B. Hannsgen, O.J. Staffans, R.L. Wheeler. Rational Approximations of Transfer Functions of Some Viscoelastic Rods with Applications to Robust Control. J. Dynam. Control Systems 5 (1999), no. 2, 255--302.
We study rational approximations of the transfer function $\hat P$ of a uniform or nonuniform viscoelastic rod undergoing torsional vibrations that are excited and measured at the same end. The approximation is to be carried out in a way that is appropriate, with respect to stability and performance, for the construction of suboptimal rational stabilizing compensators for the rod. The function $\hat P$ can be expressed as $\hat P(s) = s^{-2}g(\beta^2(s))$, where $g$ is an infinite product of fractional linear transformations and $\beta$ is a (generally transcendental) function that characterizes a particular viscoelastic material. First, $g(\beta^2)$ is approximated by its partial products $g_N(\beta^2)$. For relevant values of $\beta^2$, convergence rates for $g_N$ are analyzed in detail. Convergence suitable for our problem requires the introduction of a new irrational convergence factor, which must be approximated separately. In addition, the fractional linear factors in $\beta^2(s)$ that appear in $g_N(\beta^2(s))$ must be replaced by something rational. When the damping is weak it is possible to do this by separating the oscillatory modes from the ``creep'' modes and ignoring the latter; in general, this step remains incomplete. Some numerical data illustrating all the stages of the process as well as the final results for various viscoelastic constitutive relations are presented.
|
|
|
|
of manuscripts |
|
|