1st Edition

Sensitivity of Automatic Control Systems

By Efim Rozenwasser, Rafael Yusupov Copyright 1999

    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.

    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


    Efim Rozenwass, Rafael Yusupov

    "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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