Michael P. Polis

An example on the effect of time delays in boundary feedback stabilization of wave equations

This note is concerned with the erect of time delays in boundary feedback stabilization schemes for wave equations. The question to be addressed is whether such delays can destabilize a system which is uniformly asymptotically stable in the absence of delays.

Robust stability for time-delay systems: the edge theorem and graphical tests

The robust stability problem is discussed for a class of uncertain delay systems where the characteristic equations involve a polytope P of quasi-polynomials (i.e. polynomials in one complex variable and exponential powers of the variable). Given a set D in the complex plane, the goal is to find a constructive technique to verify whether all roots of every quasi-polynomial in P belong to D (that is, to verify the D-stability of P). First it is demonstrated by counterexample that Kharitonovs theorem does not hold for general delay systems. Next it is shown that under a mild assumption on the set D a polytope of quasi-polynomials is D-stable if and only if the edges of the polytope are D-stable. This extends the edge theorem for the D-stability of a polytope of polynomials. The third result gives a constructive graphical test for checking the D-stability of a polytope of quasi-polynomials which is especially simple when the set D is the open left-half plane. An application is given to demonstrate the power of the results. >

Parameter identification in distributed systems: A synthesizing overview

This paper surveys the distributed system parameter identification problem and concludes that it can be treated as a series of largely independent subproblems, each of which must be considered in any attempt to treat the problem in applications. An approach is discussed which treats in a unified manner all the inherent subproblems. An annotated bibliography of the literature in the field analyzes the contributions of the various authors to each step in the solution of problems of parameter identification in distributed systems. The applications of existing techniques are discussed, and the paper closes with conclusions and recommendations for future work in the field.

Introduction to the parametric approach to robust stability

Recent results relating to the parametric approach to robust stability are discussed. The general problem of robust stability is defined, and a brief review of Kharotinov-type, edge, and zero-exclusion results is given. Several open research directions are indicated, followed by some remarks on the potential of the approach.<<ETX>>

On parameter identification for distributed systems using Galerkin's criterion

A method is presented for estimating parameters in distributed parameter systems. The system is assumed to be modeled by a set of partial differential equations whose form is known to within a set of unknown constant parameters. Galerkins Method is used to transform the partial differential equations into a set of ordinary differential equations. The approach to the identification problem is given in a step by step procedure. Three optimization schemes for estimating the unknown parameters are discussed. They are a steepest descent method, a search technique, and nonlinear filtering.

An overview of recent results on the parametric approach to robust stability

A discussion is presented of results relating to the parametric approach to robust stability. The general problem of robust stability is defined, and a review of Kharitonov-type and edge theorems, zero exclusion results, interval matrix stability, maximal perturbation bounds, multilinear and nonlinear perturbations, time delay systems, and numerical/graphical approaches is presented. Some open research directions are indicated, and the future of the approach is discussed.<<ETX>>

The distributed system parameter identification problem: A survey of recent results

This paper will survey the recent results concerning the Distributed System Parameter Identification Problem (DSPIP). This survey covers roughly the last six years, i.e. that period following the publication of a review paper by Polis and Goodson [70] treating the same subject.

Battery Cell Identification and SOC Estimation Using String Terminal Voltage Measurements

A battery system consists of many battery cells or modules that may have different characteristics. To achieve reliable, efficient, and extended utilization of battery systems, the battery management system (BMS) must keep track of individual cell-level dynamics, state of charge (SOC), state of health (SOH), failure status, and life-expectancy prediction. Current battery technology employs cell or module-level voltage sensors, with high costs for sensors and packaging, and substantial reliability issues. This paper introduces new methods that utilize existing cell-balancing circuits to estimate an individual cells voltage and current from battery string terminal voltage/current measurements. This is achieved by actively controlling balancing circuits to create partial observability for battery cell subsystems. Control strategies, estimation algorithms, and their key properties are developed. Some typical battery model structures are used to illustrate the usage of the methods.

The edge theorem and graphical tests for robust stability of neutral time-delay systems

Abstract In this paper we consider the robust stability problem for a class of uncertain neutral time-delay systems where the characteristic equations involve a poly tope P of quasipoly neutrals of neutral type. Given a stability region D in the complex plane our goal is to find a constructive technique to verify whether all roots of every quasipolynomial in P belong to D (that is, to verify the D-stability of P). Our first result is that, under a mild assumption on the stability region D, P is D-stable if and only if the edges of P are D-stable. Hence, the D-stability problem of a higher dimensional polytope is reduced to the D-stability problem of a finite number of pairwise convex combinations of vertices. This extends the “Edge Theorem” developed by Bartlett, Hollot and Lin [BHL88] and Fu and Barmish [FB88] for the D-stability of a poly tope of polynomials and that of Fu, Olbrot and Polis [FOP88] for a poly tope of quasipolynomials. Our second result gives effective graphical tests for checking the D-stability of a polytope of quasipolynomials of neutral type when the set D is any open left half plane. The graphical test is based on the frequency response plots of some transfer functions associated with the vertices.

Source Identification for Parabolic Equations

AbstractThis paper treats an inverse problem of source identification in systems modeled by partial differential equations of parabolic type. Regularization procedures and recursive estimation algorithms are developed to estimate the location and the intensity of the source.