Stability, Stochastic Stationarity and Generalized Lyapunov Equations for Two-Point Boundary-Value Descriptor Systems,

Abstract

This paper introduces the concept of internal stability for two-point boundary-value descriptor systems (TPBVDSs). Since TPBVDSs are defined only over a finite interval, the concept of stability is not easy to formulate for these systems. The definition which is used here consists in requiring that as the length of the interval of definition increases, the effect of boundary conditions on states located close to the center of the interval should go to zero. Stochastic TPBVDSs are studied, and the property of stochastic stationarity is characterized in terms of a generalized Lyapunov equation satisfied by the variance of the boundary vector. A second generalized Lyapunov equation satisfied by state variance of a stochastically stationary TPBVDS is also introduced, and the existence and uniqueness of positive definite solutions to this equation is then used to characterize the property of internal stability. Keywords: Stability, Two-point boundary value problems. (hde)

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Document Details

Document Type
Technical Report
Publication Date
Mar 03, 1988
Accession Number
ADA195645

Entities

People

  • Alan S. Willsky
  • Bernard C. Lévy
  • Ramine Nikoukhah

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Coordinate Systems
  • Covariance
  • Cross Correlation
  • Decomposition
  • Difference Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Human Behavior
  • Noise
  • Random Variables
  • Riccati Equation
  • Standards
  • Stationary
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Linear Algebra
  • Regression Analysis.