Informatica

This paper considers the control problem of a class of linear hereditary systems subjected to a nonlinear (perhaps) time-varying controller. The absolute stability for a class of nonlinear time-varying controllers are investigated. Sufficient conditions for absolute stability and hyperstability are given.

This paper addresses the study of the controllability and stability of the equilibrium in economic models which relate the unemployment level to the government expenditure. The interesting cases when the government expenditure is either bounded or a linear function of the national income are specifically considered. The relationships between both variables, namely, unemployment growth level and government expenditure is obtained by considering a Keynesian static model for the national income as well as a differential unemployment-inflation model of Phillips type. Both models are used to derive a new combined one by eliminating the common variable “taxes” which is driven by the investment and government expenditure.

Part II deals with the design problem of generalized linear controllers for linear systems with after-effect so that the resulting closed-loop system is globally uniformly asymptotically stable in the Lyapunov's sense. The controllers are universal in the sense that they include the usual delays (namely, point, distributed and mixed point-distributed delays) which can be finite, infinite or even time-varying. The stability is formulated in terms of sufficient conditions depending, in general, on the system parameters and delays. It is shown that a stabilizing controller can be designed by using the well-known Kronecker product of matrices provided that a stabilizing controller exists in the absence of external (or, input) delay.

This paper deals with the design problem of generalized linear controllers for linear systems with after-effect so that the resulting closed-loop system is globally uniformly asymptotically stable in the Lyapunov's sense. The controllers are universal in the sense that they include the usual delays (namely, point, distributed and mixed point-distributed delays) which can be finite, infinite or even time-varying. In Part I of the paper, some preliminary concepts and results on stabilizability are given.

This paper addresses the application of convergence rules of gradient-type discrete algorithms to discrete adaptive control algorithms for linear time-invariant systems, which are based on Lyapunov's – like functions, in order to improve the transient performances based on fast adaptation. In particular, the adaptation covergence is increased as a generalized or filtered error increases through the application of Armijo rule for regulating the decrease of each Lyapunov's-like function on which the particular adaptation algorithm is based. The proposed scheme can be implemented with minor modifications in systems subject to unmodelled dynamics if some weak knowledge on such a dynamics is available consisting of upper-bounds of the dimension and norm of the unmodelled parameter vector.

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

The paper describes the use of adaptive and non-periodic sampling in different fields of System Theory and Control. The review is organized in a very comprehensive way and it presents results of the last thirty years about the problem of signal applications using as main tool adaptive sampling schemes including results is the improvement of the transient behaviors. Also, related results are presented about the use of non-periodic sampling in compensation as an alternative design to the well-known frequency domain methods and about the choice of the sampling points in order to improve the transmission of measuring and/or rounding errors towards the results when studying the properties of dynamic systems such as controllability, observability and identifiability.

This paper presents a direct adaptive, control algorithm, based on a σ-modification rule, which is robust respect to additive and multiplicative plant unmodelled dynamics for plants involving both internal (i.e., in the state) and external (i.e., in the output or input) known point delays. Several adaptive controller structures are given and analyzed for the case of plants with unknown parameters while being assumed that the nominal plant is of known order and relative order. The parametrized parts of two of the controller structures involve delays while those of the two remaining controllers are delay-free. However, auxiliary compensating signals which weight the plant input and output integrals are incorporated in all the controller structures for stabilization purposes. It is proved that, if the unmodelled dynamics is sufficiently small at low frequencies, then the adaptive algorithm guarantees boundedness of all the signals in the closed-loop system.

This paper presents a robust control algorithm for plants involving both internal (i.e., in the state) and external (i.e., in the output or input) known point delays. Several stabilizing controller structures are given and analyzed for the case of perfectly modelled plants with known parameters. The plant is assumed to be of known order and relative order. The parametrized parts of two of the controller structures involve delays while those of the two remaining controllers are delay-free. However, auxiliary compensating signals which weight the plant input and output integrals are incorporated in all the controller structures for stabilization and model matching purposes.

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.