Accession Number:

AD0731281

Title:

Almost-Sure Stability of Randomly-Sampled Systems,

Descriptive Note:

Corporate Author:

MICHIGAN UNIV ANN ARBOR COMPUTER INFORMATION AND CONTROL ENGINEERING

Personal Author(s):

Report Date:

1971-10-01

Pagination or Media Count:

129.0

Abstract:

Considered in the document are autonomous closed loop systems described by constant co-efficient matrix-vector differential equations, with a zero memory nonlinear element in the feedback path, and containing a sample-and-hold device whose sampling times are described by a stationary point process. For such systems, the author studies sufficiency conditions under which almost sure asymptotic stability is attained. These are given in terms of a stability sector of the Popov type for the nonlinearity. Stochastic Lyapunov functions are constructed as a means of finding the stability criterion. An explicit formulation is given for determining a sub-optimal quadratic Lyapunov function which results in a sector larger than any obtained by others. An algorithm is also found to prodice a sub-optimum over a larger class of possible Lyapunov functions this extends the sector even further. The system under consideration can also be described in terms of stochastic operators. This approach yields stability results through a convergence theorem for sequences of random variables centered at conditional expectations. Author

Subject Categories:

  • Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE