25 research outputs found
On stable cones of polynomials via reduced Routh parameters
summary:A problem of inner convex approximation of a stability domain for continuous-time linear systems is addressed in the paper. A constructive procedure for generating stable cones in the polynomial coefficient space is explained. The main idea is based on a construction of so-called Routh stable line segments (half-lines) starting from a given stable point. These lines (Routh rays) represent edges of the corresponding Routh subcones that form (possibly after truncation) a polyhedral (truncated) Routh cone. An algorithm for approximating a stability domain by the Routh cone is presented
Geometry of physical dispersion relations
To serve as a dispersion relation, a cotangent bundle function must satisfy
three simple algebraic properties. These conditions are derived from the
inescapable physical requirements to have predictive matter field dynamics and
an observer-independent notion of positive energy. Possible modifications of
the standard relativistic dispersion relation are thereby severely restricted.
For instance, the dispersion relations associated with popular deformations of
Maxwell theory by Gambini-Pullin or Myers-Pospelov are not admissible.Comment: revised version, new section on applications added, 46 pages, 9
figure
A new computational approach to the synthesis of fixed order controllers
The research described in this dissertation deals with an open problem concerning
the synthesis of controllers of xed order and structure. This problem is encountered
in a variety of applications. Simply put, the problem may be put as the
determination of the set, S of controller parameter vectors, K = (k1; k2; : : : ; kl),
that render Hurwitz a family (indexed by F) of complex polynomials of the form
fP0(s; ) + Pl
i=1 Pi(s; )ki; 2 Fg, where the polynomials Pj(s; ); j = 0; : : : ; l
are given data. They are specied by the plant to be controlled, the structure of the
controller desired and the performance that the controllers are expected to achieve.
Simple examples indicate that the set S can be non-convex and even be disconnected.
While the determination of the non-emptiness of S is decidable and amenable
to methods such as the quantier elimination scheme, such methods have not been
computationally tractable and more importantly, do not provide a reasonable approximation
for the set of controllers. Practical applications require the construction of a
set of controllers that will enable a control engineer to check the satisfaction of performance
criteria that may not be mathematically well characterized. The transient
performance criteria often fall into this category. From the practical viewpoint of the construction of approximations for S, this
dissertation is dierent from earlier work in the literature on this problem. A novel
feature of the proposed algorithm is the exploitation of the interlacing property of
Hurwitz polynomials to provide arbitrarily tight outer and inner approximation to
S. The approximation is given in terms of the union of polyhedral sets which are
constructed systematically using the Hermite-Biehler theorem and the generalizations
of the Descartes' rule of signs
Model-based and data-based frequency domain design of fixed structure robust controller: a polynomial optimization approach
L'abstract è presente nell'allegato / the abstract is in the attachmen
Target Recognition Using Late-Time Returns from Ultra-Wideband, Short-Pulse Radar
The goal of this research is to develop algorithms that recognize targets by exploiting properties in the late-time resonance induced by ultra-wide band radar signals. A new variant of the Matrix Pencil Method algorithm is developed that identifies complex resonant frequencies present in the scattered signal. Kalman filters are developed to represent the dynamics of the signals scattered from several target types. The Multiple Model Adaptive Estimation algorithm uses the Kalman filters to recognize targets. The target recognition algorithm is shown to be successful in the presence of noise. The performance of the new algorithms is compared to that of previously published algorithms