Sensitivity of Automatic Control Systems: 1st Edition (Hardback) book cover

Sensitivity of Automatic Control Systems

1st Edition

By Efim Rozenwasser, Rafael Yusupov

CRC Press

456 pages

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Hardback: 9780849322938
pub: 1999-11-23
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Although it arose much earlier in a variety of contexts, sensitivity theory became an independent branch of science in the sixties. Since then, researchers from around the world have continued to make great strides in both the theory and its applications. However, much of the work of Russian scientific schools and specialists remain unknown in the West.

Sensitivity of Control Systems summarizes the results of the authors and their disciples in sensitivity theory, addressing the basic notions of the theory and the problem of selecting technical parameters of systems. The authors formulate problems for actual technical systems and their models, and establish relations between sensitivity theory and classical stability problems. They offer a significant, general theory for investigating the sensitivity of boundary problems and use elements of this theory for sensitivity analysis of solutions to nonlinear programming and variational calculus problems, as well as oscillatory processes. The book also presents general investigation methods for discontinuous systems, including those described by operator models.

Full of powerful new methods and results, this book offers a unique opportunity for those in theoretical investigation and in the design, testing, and exploitation of various control systems to explore the work of Russia's leading researchers in sensitivity theory. Furthermore, its techniques for parametric perturbation investigation, Sensitivity of Control Systems will prove useful in fields outside of control theory, including oscillation theory, motion dynamics, and mathematical economy.


"This book covers the sensitivity of both linear and nonlinear discontinuous systems…Rigorously justifies the use of first approximations-which are the basis of most applied problems."

- Mechanical Engineering

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Table of Contents


Parametric Models

State Variables and Control System Parameters

Parametric Models of Control Systems

Sensitivity Functions and their Applications

Finite-Dimensional Continuous Systems

Finite-Dimensional Continuous Systems Depending on a Parameter

Second Lyapunov's Method in Sensitivity Theory

Sensitivity on Infinite Time Intervals

Sensitivity Analysis of Self-Oscillating Systems in the Time Domain

Sensitivity of Non-Autonomous Systems

Sensitivity of Solutions of Boundary Value Problems

Finite-Dimensional Discontinuous Systems

Sensitivity Equations for Finite Dimensional Discontinuous Systems

Sensitivity Equations for Relay Systems

Sensitivity Equations for Pulse and Relay-Pulse Systems

Discontinuous Systems Given by Operator Models

Operator Parametric Models of Control Systems

Operator Models of Discontinuous Systems

Sensitivity of Operator Models

Sensitivity Equations of Relay and Pulse Systems

Non-Time Characteristics

Sensitivity of Transfer Function and Frequency Response of Linear Systems

Sensitivity of Zeros and Poles

Sensitivity of Eigenvalues and Eigenvectors of Linear Time Invariant Control Systems

Sensitivity of Integral Quality Indices

Indirect Characteristics of Sensitivity Functions

Sensitivity Invariants

Sensitivity Invariants of Time Characteristics

Root and Transfer Function Sensitivity Invariants

Sensitivity Invariants of Frequency Responses

Sensitivity Invariants of Integral Estimates

Sensitivity Invariants for Gyroscopic Systems

Sensitivity of Mathematical Programming

Sensitivity of Linear Programming Problems

Sensitivity of Optimal Solutions of Non-Linear Programming Problems

Sensitivity of a Simplest Variational Problem

Sensitivity of Variational Problems with Flexible Boundaries and Corner Points

Sensitivity of Variational Problems on Conditional Extremum

Applied Sensitivity Problems

Direct and Inverse Problems of Sensitivity Theory

Identification of Dynamic Systems

Distribution of Parameter Tolerance

Synthesis of Insensitive Systems

Numerical Solution of Sensitivity Equations

About the Authors/Editors

Efim Rozenwass, Rafael Yusupov

About the Series

Control Series

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