Absolute Stability Of Control System Research Articles

Absolute stability of control system with piezo actuator for nanotechnology and robotics

The work considers the absolute stability of the control system with the piezoactuator for nanotechnology, robotics, nanomedicine, astronomy, adaptive optics and electron microscopy. In the control system with the hysteresis characteristic for the deformation of the piezoactuator, the set of the equilibrium positions of the system is the straight line segment. Using the Yakubovich criterion for the control system, the absolute stability of the system with the piezoactuator for nanotechnology and robotics is obtained.

Absolute Stability of Control System with Electro Magneto Elastic Actuator for Nano Science and Nano Biomedicine Research

The stationary set of the control system of the hysteresis deformation of the electro magneto elastic actuator is the segment of the straight line. The aim of this work is to determine the condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator in automatic nanomanipulators for Nano science and Nano biomedicine research. The frequency methods for Lyapunov stable control system are used to calculate the condition the absolute stability of the control system with electro magneto elastic actuator. In result we obtained the condition of the absolute stability on the derivative for the control system with the electro magneto elastic actuator in automatic nanomanipulators for Nano science and Nano biomedicine research.

Absolute Stability of Control System with Electro Magneto Elastic Actuator for Nanobiomedicine

In this work the condition of the absolute stability on the derivative for control system of the deformation of the electro magneto elastic actuator is calculated..

Condition Absolute Stability of Control System with Electro Elastic Actuator for Nano Bioengineering and Microsurgery

The condition absolute stability on the derivative for the control system deformation of the electro elastic actuator for nano bioengineering and microsurgery is determined..

On a program manifold’s stability of one contour automatic control systems

AbstractMethodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold’s absolute stability of one contour automatic control systems are obtained. The Hurwitz’s angle of absolute stability was determined. The sufficient conditions of program manifold’s absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov’s second method.

Hidden Oscillations in Dynamical Systems. 16 Hilbert’s Problem, Aizerman’s and Kalman’s Conjectures, Hidden Attractors in Chua’s Circuits

The present survey is devoted to efficient methods for localization of hidden oscillations in dynamical systems. Their application to Hilbert’s sixteenth problem for quadratic systems, Aizerman’s problem, and Kalman’s problem on absolute stability of control systems, and to the localization of chaotic hidden attractors (the basin of attraction of which does not contain neighborhoods of equilibria) is considered. The synthesis of the describing function method with the applied bifurcation theory and numerical methods for computing hidden oscillations is described.

Hidden oscillations in nonlinear control systems

AbstractThe method of harmonic linearization, numerical methods, and the applied bifurcation theory together discover new opportunities for analysis of hidden oscillations of control systems. In the present paper new analytical-numerical algorithm for hidden oscillation localization is discussed. Counterexamples construction to Aizerman's conjecture and Kalman's conjecture on absolute stability of control systems are considered.

Correctors in control systems for piezo nanomotors

The conditions of absolute stability of control systems for piezo nanomotors are obtained, for longitudinal and transverse piezo effects, in the case of determinate and random perturbations. Correctors are chosen to ensure quality of the nanomotors’ control system and the required oscillation properties.

Absolute stability of control systems for electromagnetoelastic nanodrives

Absolute stability of control systems for electromagnetoelastic nanodrives

Absolute stability of control systems for electromagnetoelastic nanodrives

Absolute stability of control systems for electromagnetoelastic nanodrives

ABSOLUTE STABILITY OF CONTROL SYSTEM WITH MULTI-NONLINEAR FEEDBACK TERMS

In this paper, the absolute stability of control systems with multi nonlinear feedback terms are studied. The sufficient and necessary conditions of absolute stability are obtained. Some applied sufficient conditions of absolute stability are given.

Comments on ‘on absolute stability and the aizerman conjecture’

This paper discusses the absolute stability of control system. We point out that Theorem 2 in the paper by Grujic is not correct.

Absolute stability of control systems with retarded argument

By Lyapunov's direct method we investigate the behavior of systems of automatic control with one nonlinearity and retarded argument. Sufficient criteria for the absolute stability of systems for an arbitrary magnitude of the retardation are obtained.

SOME SYSTEM THEORY IDEAS CONNECTED WITH THE STABILITY PROBLEM

Abstract In this paper some connections of mathematical system theory with the problem of absolute stability of control systems are pointed out. The absolute stability problem was formulated in the early 1940s starting from some practical control problems. The considerable development of this problem in the last 25 years has been profitable for mathematical system theory. At the same time concepts of system theory provided an adequate context for a deep understanding of this problem. Such system theory concepts as blocks, interconnections, isomorphism between time domain representations, and complex domain characteristics showed themselves very useful in absolute stability and hyperstability studies. Among the main contributions of absolute stability and hyperstability studies to mathematical system theory development one can cite the concept of “block plus integral index” and the system theory interpretation of Bochner's theorem on positive functions.

Absolute stability of control systems with many sector and slope-restricted non-linearities

The absolute stability of free control systems with many sector and slope-restricted non-linearities is considered. The sufficient conditions derived include a new stability criterion in the frequency domain. By the inclusion of the information on the slopes of the non-linearities it is shown that improved results can be obtained over the Popov criterion for several examples.