Accession Number : ADA195645

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

Corporate Author : MASSACHUSETTS INST OF TECH CAMBRIDGE LAB FOR INFORMATION AND DECISION SYSTEMS

Personal Author(s) : Nikoukhah, Ramine ; Levy, Bernard C ; Willsky, Alan S

PDF Url : ADA195645

Report Date : 03 Mar 1988

Pagination or Media Count : 52

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)

Descriptors :   *BOUNDARY VALUE PROBLEMS, *LYAPUNOV FUNCTIONS, EQUATIONS, INTERNAL, INTERVALS, LENGTH, STABILITY, VARIATIONS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE