Informatica

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.

In the practice of metal treatment by cutting it is frequently necessary to deal with self-excited oscillations of the cutting tool, treated detail and units of the machine tool. In this paper are presented differential equations with the delay of self-excited oscillations. The linear analysis is performed by the method of D-expansion. There is chosen an area of asymptotically stability and area D2. It is prove that, in the area D2 the stable periodical solution appears. The non-linear analysis is performed by the theory of bifurcation. The computational experiment of metal cutting process and results of these experiments are presented.

New formulae providing exact explicit solutions for a class of scalar delayed systems are given.

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.

The convergence properties of some LOD schemes are considered. New stability estimates with respect to boundary conditions are proved. These results are used to investigate the accuracy of LOD schemes when no special boundary correction technique is used for the realization of LOD schemes. The accuracy of LOD schemes with corrected boundary conditions is also investigated. Results of the computational experiment are given.