Pub. online:1 Jan 2016Type:Research ArticleOpen Access
Volume 27, Issue 2 (2016), pp. 323–334
This paper reviews the interplay between global optimization and probability models, concentrating on a class of deterministic optimization algorithms that are motivated by probability models for the objective function. Some complexity results are described for the univariate and multivariate cases.
Pub. online:1 Jan 2011Type:Research ArticleOpen Access
Volume 22, Issue 4 (2011), pp. 471–488
We describe an adaptive algorithm for approximating the global minimum of a continuous univariate function. The convergence rate of the error is studied for the case of a random objective function distributed according to the Wiener measure.
Pub. online:1 Jan 2006Type:Research ArticleOpen Access
Volume 17, Issue 4 (2006), pp. 565–576
Robust stability results for nominally linear hybrid systems are obtained from total stability theorems for purely continuous-time and discrete-time systems. The class of hybrid systems dealt with consists of, in general, coupled continuous-time and digital systems subject to state perturbations whose nominal (i.e., unperturbed) parts are linear and time-varying, in general. The obtained sufficient conditions on robust stability are dependent on the values of the parameters defining the over-bounding functions of the uncertainties and the weakness of the coupling between the analog and digital sub-states provided that the corresponding uncoupled nominal subsystems are both exponentially stable.
Pub. online:1 Jan 1994Type:Research ArticleOpen Access
Volume 5, Issues 3-4 (1994), pp. 385–413
This paper establishes sufficient conditions for stability of linear and time-invariant delay differential systems including their various usual subclasses (i.e., point, distributed and mixed point-distributed delay systems). Sufficient conditions for stability are obtained in terms of the Schur's complement of operators and the frequency domain Lyapunov equation. The basic idea in the analysis consists in the use of modified Laplace operators which split the characteristic equation into two separate multiplicative factors whose roots characterize the system stability. The method allows a simple derivation of stabilizing control laws.