Results

**1 - 8**of**8**### Path Integrals And Stability

, 1998

"... A path integral associated with a dynamical system is an integral of a memoryless function of the system variables which, when integrated along trajectories of the system, depends only on the value of the trajectory and its derivatives at the endpoints of the integration interval. In this paper we s ..."

Abstract
- Add to MetaCart

A path integral associated with a dynamical system is an integral of a memoryless function of the system variables which, when integrated along trajectories of the system, depends only on the value of the trajectory and its derivatives at the endpoints of the integration interval. In this paper we study path independence for linear systems and integrals of quadratic differential forms. These notions and the results are subsequently applied to stability questions. This leads to Lyapunov stability theory for autonomous systems described by high-order differential equations, and to more general stability concepts for systems in interaction with their environment. The latter stability issues are intimately related to the theory of dissipative systems.

### A New Genetic Algorithm using Pareto Partitioning Method for Robust Partial Model Matching PID Design with Two Degrees of Freedom

"... : In this paper we present a new genetic algorithm (GA) using pareto partitioning method and apply this GA to solving the design problem of the robust PID controller with two degrees of freedom based on the partial model matching approach. This design problem is formulated as two objective minima ..."

Abstract
- Add to MetaCart

: In this paper we present a new genetic algorithm (GA) using pareto partitioning method and apply this GA to solving the design problem of the robust PID controller with two degrees of freedom based on the partial model matching approach. This design problem is formulated as two objective minimax optimization problem. Therefore we need to generate a pareto optimal set that is properly distributed in the neighborhood of the trade-off surface. The proposed GA is able to uniformely control the convergence of this pareto optimal solutions. Some numerical examples show the effectiveness of the present method. 1. Introduction Most industrial processes are controlled by PID (that has Propotional, Integral and Derivative actions) or I-PD controllers, because these controllers have simple construction and easy to tune. Many auto-tuning method of PID controller based on Ziegler-Nichols and so on have been developed consequently[1, 2]. These methods of tuning parameters of PID controller...

### Minkowski Combinations of Complex Sets-- Geometry, Algorithms, and Applications

"... x1. Preamble The evolution of mathematics has been shaped by a constantly-changing relationship between algebra and geometry. These subjects have, at times, vied for supremacy in mathematical discourse-- at other times, they have served to reveal profound new insights and perspectives to each other. ..."

Abstract
- Add to MetaCart

x1. Preamble The evolution of mathematics has been shaped by a constantly-changing relationship between algebra and geometry. These subjects have, at times, vied for supremacy in mathematical discourse-- at other times, they have served to reveal profound new insights and perspectives to each other. In the first mathematically-adept civilization, that of ancient Mesopotamia, skilled algebraists were fully conversant with the manipulation of equations (and in certain cases the extraction of their roots), but were apparently less interested in problems of geometry. Conversely, the ancient Greeks sought refuge from the mysteries of irrational numbers (an inevitable consequence of basic algebraic operations) in purely geometrical constructions. Rene Descartes (1596-1650) liberated geometry from the confines of mere ruler-and-compass constructions. The arithmetization of geometry, through the introduction of coordinates, opened new worlds of unimagined subtlety and intricacy to systematic exploration. With the development of

### The Kharitonov theorem and its applications in symbolic mathematical computation

, 1997

"... this paper we deal with the problem of diagnosing if a polynomial has such behaviour. In the past, various results deriving bounds of root displacement of a complex polynomial from the size of perturbations of the coefficients were published (e.g., the ones cited in (Marden 1966)). Conversely, theor ..."

Abstract
- Add to MetaCart

this paper we deal with the problem of diagnosing if a polynomial has such behaviour. In the past, various results deriving bounds of root displacement of a complex polynomial from the size of perturbations of the coefficients were published (e.g., the ones cited in (Marden 1966)). Conversely, theorems elucidating the relationship between coefficient perturbations and root locations are rare, or lead to impractical algorithms in terms of computational costs. One of the few exceptions is the seminal result by V. L. Kharitonov (1978a). He showed that for interval polynomials with real coefficients, it is necessary and sufficient to test just four special members of the polynomial family in order to decide that all polynomials have their roots in the left half of the Gaussian plane (i.e., that they are Hurwitz). He extended his result to complex coefficients in a follow-up paper; eight test polynomials are required in this case. Sensitivity analysis is an important methodolgy for dealing with symbolic/numeric problem formulations. The inputs are given with imprecise, i.e., floating point coefficients and the algorithms must decide whether within a given perturbation of the coefficients problem instances exist that satisfy the wanted properties. A classical problem is the perturbation of the coefficients to make inconsistent system of linear equations solvable.

### Military Institutions of University Education,

"... Abstract:- This paper presents a new contribution in the problem of computing the stability margin of 2-D (two-dimensional) discrete systems. The method, using the "Resultant technique " instead of a typical minimization procedure ([9]), is actually an improvement of the method of [9]. ..."

Abstract
- Add to MetaCart

Abstract:- This paper presents a new contribution in the problem of computing the stability margin of 2-D (two-dimensional) discrete systems. The method, using the "Resultant technique " instead of a typical minimization procedure ([9]), is actually an improvement of the method of [9].