S. Mossaheb

Bio: S. Mossaheb is an academic researcher from University of Bradford. The author has contributed to research in topics: Multivariable calculus & Nonlinear system. The author has an hindex of 5, co-authored 8 publications receiving 102 citations.

Application of a method of averaging to the study of dithers in non-linear systems

Abstract: Using averaging methods of the theory of differential equations, the effects of the injection of high frequency signals, known as dithers, in non-linear systems is studied. The behaviour of the dithered system is compared with that of a smoothed one, whose non-linearity is the convolution of the dither distribution function and the original non-linearity. It is proved that if over a given time interval the smoothed system has a bounded solution, then so does the dithered system, provided that the dither frequency is high enough, and the output of the two systems can be made as close as desired. Moreover, if the trajectories of the smoothed system are asymptotically attracted to a compact set, for example a stable orbit or singular point, then the trajectories of the dithered system can be made to remain close to this set. In particular, a satisfactory explanation of quenching of limit cycldes is botained in this way. The analysis takes account of certain disturbances which might arise due to the injection...

Passivity and the design of sampled regulators for uncertain systems

Abstract: A method of designing robust sampled regulators for open-loop stable, linear, time-invariant, multivariable plants is given. The design procedure requires only the knowledge of the open-loop step response of the system and is independent of its structure. It allows the imposition of constraints on the maximum excursion of the inputs to the plant. The stability of the closed-loop system follows from its passivity and this, in turn, is obtained from a classical theorem of W. H. Young in the theory of trigonometric series. As a result it turns out that the stability of the algorithm is independent of the sampling rate. Moreover, the method of proving stability enables one to estimate the size of plant perturbations and/or measurement errors that can be tolerated before the onset of instability. Finally, a partial answer, leading to a Lyapunov-type equation, is also given to the question of the optimal choice of control parameters.

A Nyquist type stability criterion for linear multivariable delayed systems

Abstract: Using the theory of analytic functions the stability of linear multivariable systems defined by a set of delayed differential equations is considered. It is shown that such systems may be described by transfer function matrices which determine their stability. The theory of coprime factorization of transfer functions is used to extend some of the concepts of algebraic system theory to the delayed case. These results are then used to develop a Nyquist type criterion for the analysis of feedback stability under proportional and dynamic feedback. The theoretical development is illustrated by an example of a two state system with three unstable poles.

Extensions to the design of sampled integrating regulators

Abstract: The stability properties and design rules for a class of robust integrating regulators are considered. Passivity arguments are employed to define bounds on the parameters of an extended PID regulator and to establish the robustness of the closed-loop stability properties in the presence of sector-bounded non-linear elements in the feedback loop. This approach allows linear and non-linear single-input/single-output and multi-input/multi-oulput systems to be considered in the same framework.

A new approach to the prediction of limit cycles

Abstract: The describing function method is commonly used for the prediction of limit cycles in non-linear systems. This method is based upon the representation of signals by a Fourier series, and assigning a gain to the non-linear component derived from its response to a sinusoidal input, In this paper we show that a different approach is feasible which in some respects is the dual of the describing function method. The signals are analysed into a Walsh scries, and a gain is assigned to the linear component of the system derived from its response to a square, wave. In many instances the method is likely to give more accurate predictions of limit cycling.

Delay Robustness in Non-Identical Multi-Agent Systems

Abstract: We investigate the robustness of consensus protocols on sensor networks to different types of feedback delays. We provide set-valued conditions for consensus of linear Multi-Agent Systems (MAS) with nonidentical agent dynamics and heterogeneous delays. These conditions consider different feedback delay configurations and are robust and scalable to unknown, arbitrary large topologies and unknown but bounded self-delays and communication delays. Moreover, we provide consensus conditions for relative degree two MAS with different feedback delays in order to illustrate the applicability of these set-valued conditions.

Stability of dithered non-linear systems with backlash or hysteresis

Abstract: A study is conducted of the effect of dither on the nonlinear element of a single-input single-outout feedback system. Nonlinearities are considered with memory (backlash, hysteresis), in the feedforward loop; a dither of a given amplitude is injected at the input of the nonlinearity. The nonlinearity is followed by a linear element with low-pass characteristic. The stability of the dithered system and an approximate equivalent system (in which the nonlinearity is a smooth function) are compared. Conditions on the input and on the dither frequency are obtained so that the approximate-system stability guarantees that of the given hysteretic system.