Search results for "Lyapunov function"
showing 10 items of 104 documents
An LMI approach to vibration control of base-isolated building structures with delayed measurements
2010
In this article, we address a convex optimisation approach to the problem of state-feedback H∞ control design for vibration reduction of base-isolated building structures with delayed measurements, where the delays are time-varying and bounded. An appropriate Lyapunov-Krasovskii functional and some free-weighting matrices are utilised to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities. The controller, which guarantees asymptotic stability and an H∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated by means of simula…
Hierarchical fuzzy/Lyapunov control for horizontal plane trajectory tracking of underactuated AUV
2010
A new hierarchical closed loop fuzzy control system for horizontal plane trajectory tracking of underactuated Autonomous Underwater Vehicles (AUV) is presented. A model for the AUV is formulated introducing a polar coordinates transformation for the velocities in the body fixed frame. It is employed to control the unactuated sway direction, the longitudinal position and the yaw by using the surge force and the yaw torque only. The highest level control is developed by employing a fuzzy inference system for obtaining the guidance control laws. The properties of the fuzzy system ensure forward surge velocity, fast convergence and Lyapunov's stability of the motion errors. A new low level kine…
A nonlinear observer for rotor flux estimation considering magnetic saturation effects in induction motor drives
2015
This paper proposes a non-linear observer for In- duction Machine (IM) drives which takes into consideration the saturation effects. The non-linear observer is based on an original formulation of the dynamic model of the IM taking into consideration the magnetic saturation of the iron core. A Lyapunov based convergence analysis is proposed in order to suitably compute the observer gain guaranteeing the stability of the observer. The proposed non-linear observer has been tested in numerical simulation and experimentally on a suitably developed test set-up. Its behaviour has been compared to that obtained with a classic Full-Order Luenberger Observer (FOLO) in variable flux working conditions…
A Nonlinear Observer for Rotor Flux Estimation of Induction Motor Considering the Estimated Magnetization Characteristic
2017
This paper proposes a nonlinear observer for induction machine drives based on space-vector dynamic model of induction machine, expressed in state form, which presents the peculiarity of taking into consideration the magnetic saturation of the iron core. This observer is particularly suitable in order to obtain high accuracy in rotor flux estimation, in both amplitude and phase position, during working conditions characterized by varying flux, among which the most important are those during electrical losses minimization. A Lyapunov-based convergence analysis is proposed in order to suitably compute the numerical observer gain guaranteeing the convergence of the estimation error. The propos…
Stability analysis and H∞ controller synthesis of discrete-time switched systems with time delay
2014
Abstract This paper studies the problems of stability analysis and H ∞ controller synthesis of switched systems with time-varying delay based on an input–output approach. The attention is focused on developing a new method to further reduce the conservatism of the existing results. The system under consideration is transformed into an interconnection system, and the scaled small gain condition for the interconnection systems is introduced. Based on the system transformation and the scaled small gain theorem, an improved delay-dependent stability criterion is proposed such that the interconnection system is asymptotically stable, which is also proved to guarantee the asymptotic stability of …
Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents
2021
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We focus on an approach, associated with the identification of a deterministic endogenous mechanism of irregular fluctuations in the economy. Using of a mid-size firm model as an example, we demonstrate the use of effective analytical and numerical procedures for calculating the quantitative characteristics of its irregular limiting dynamics based on Lyapunov exponents, such as dimension and entropy. We use an analytical approach for localization of a global at…
Perturbation of the Lyapunov spectra of periodic orbits
2012
We describe all Lyapunov spectra that can be obtained by perturbing the derivatives along periodic orbits of a diffeomorphism. The description is expressed in terms of the finest dominated splitting and Lyapunov exponents that appear in the limit of a sequence of periodic orbits, and involves the majorization partial order. Among the applications, we give a simple criterion for the occurrence of universal dynamics.
Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimensi…
2018
In this article, on the example of the known low-order dynamical models, namely Lorenz, Rossler and Vallis systems, the difficulties of reliable numerical analysis of chaotic dynamical systems are discussed. For the Lorenz system, the problems of existence of hidden chaotic attractors and hidden transient chaotic sets and their numerical investigation are considered. The problems of the numerical characterization of a chaotic attractor by calculating finite-time time Lyapunov exponents and finite-time Lyapunov dimension along one trajectory are demonstrated using the example of computing unstable periodic orbits in the Rossler system. Using the example of the Vallis system describing the El…
Exponential Transients in Continuous-Time Symmetric Hopfield Nets
2001
We establish a fundamental result in the theory of continuous-time neural computation, by showing that so called continuous-time symmetric Hopfield nets, whose asymptotic convergence is always guaranteed by the existence of a Liapunov function may, in the worst case, possess a transient period that is exponential in the network size. The result stands in contrast to e.g. the use of such network models in combinatorial optimization applications. peerReviewed
Local Capacity $H_{\infty}$ Control for Production Networks of Autonomous Work Systems With Time-Varying Delays
2010
This paper considers the problem of local capacity H∞ control for a class of production networks of autonomous work systems with time-varying delays in the capacity changes. The system under consideration is modeled in a discrete-time singular form. Attention is focused on the design of a controller gain for the local capacity adjustments which maintains the work-in-progress (WIP) in each work system in the vicinity of planned levels and guarantees the asymptotic stability of the system and reduces the effect of the disturbance input on the controlled output to a prescribed level. In terms of a matrix inequality, a sufficient condition for the solvability of this problem is presented using …