Almost-Sure Stability of Randomly-Sampled Systems

摘要

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)