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New qualitative methods for stability of delay systems

Erik I. Verriest (2001)

Kybernetika

A qualitative method is explored for analyzing the stability of systems. The approach is a generalization of the celebrated Lyapunov method. Whereas classically, the Lyapunov method is based on the simple comparison theorem, deriving suitable candidate Lyapunov functions remains mostly an art. As a result, in the realm of delay equations, such Lyapunov methods can be quite conservative. The generalization is here in using the comparison theorem directly with a different scalar equation with known...

New stability conditions for positive continuous-discrete 2D linear systems

Tadeusz Kaczorek (2011)

International Journal of Applied Mathematics and Computer Science

New necessary and sufficient conditions for asymptotic stability of positive continuous-discrete 2D linear systems are established. Necessary conditions for the stability are also given. The stability tests are demonstrated on numerical examples.

Noise Shaping in Neural Populations with Global Delayed Feedback

O. Ávila Åkerberg, M. J. Chacron (2010)

Mathematical Modelling of Natural Phenomena

The interplay between intrinsic and network dynamics has been the focus of many investigations. Here we use a combination of theoretical and numerical approaches to study the effects of delayed global feedback on the information transmission properties of neural networks. Specifically, we compare networks of neurons that display intrinsic interspike interval correlations (nonrenewal) to networks that do not (renewal). We find that excitatory and...

Non-fragile controllers for a class of time-delay nonlinear systems

Lubomír Bakule, Manuel de la Sen (2009)

Kybernetika

The paper deals with the synthesis of a non-fragile state controller with reduced design complexity for a class of continuous-time nonlinear delayed symmetric composite systems. Additive controller gain perturbations are considered. Both subsystems and interconnections include time-delays. A low-order control design system is first constructed. Then, stabilizing controllers with norm bounded gain uncertainties are designed for the control design system using linear matrix inequalities (LMIs) for...

Nonlinear analysis of vehicle control actuations based on controlled invariant sets

Balázs Németh, Péter Gáspár, Tamás Péni (2016)

International Journal of Applied Mathematics and Computer Science

In the paper, an analysis method is applied to the lateral stabilization problem of vehicle systems. The aim is to find the largest state-space region in which the lateral stability of the vehicle can be guaranteed by the peak-bounded control input. In the analysis, the nonlinear polynomial sum-of-squares programming method is applied. A practical computation technique is developed to calculate the maximum controlled invariant set of the system. The method calculates the maximum controlled invariant...

Nonlinear bounded control for time-delay systems

Germain Garcia, Sophie Tarbouriech (2001)

Kybernetika

A method to derive a nonlinear bounded state feedback controller for a linear continuous-time system with time-delay in the state is proposed. The controllers are based on an e -parameterized family of algebraic Riccati equations or on an e -parameterized family of LMI optimization problems. Hence, nested ellipsoidal neighborhoods of the origin are determined. Thus, from the Lyapunov–Krasovskii theorem, the uniform asymptotic stability of the closed-loop system is guaranteed and a certain performance...

Nonlinear feedback stabilization of a rotating body-beam without damping

Boumediène CHENTOUF, Jean-François COUCHOURON (2010)

ESAIM: Control, Optimisation and Calculus of Variations

This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear...

Nonlinear feedback stabilization of a two-dimensional Burgers equation

Laetitia Thevenet, Jean-Marie Buchot, Jean-Pierre Raymond (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the stabilization of a two-dimensional Burgers equation around a stationary solution by a nonlinear feedback boundary control. We are interested in Dirichlet and Neumann boundary controls. In the literature, it has already been shown that a linear control law, determined by stabilizing the linearized equation, locally stabilizes the two-dimensional Burgers equation. In this paper, we define a nonlinear control law which also provides a local exponential stabilization of...

Nonlinear stabilizing control of an uncertain bioprocess model

Neli Dimitrova, Mikhail Krastanov (2009)

International Journal of Applied Mathematics and Computer Science

In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a...

Nonparametric instrumental variables for identification of block-oriented systems

Grzegorz Mzyk (2013)

International Journal of Applied Mathematics and Computer Science

A combined, parametric-nonparametric identification algorithm for a special case of NARMAX systems is proposed. The parameters of individual blocks are aggregated in one matrix (including mixed products of parameters). The matrix is estimated by an instrumental variables technique with the instruments generated by a nonparametric kernel method. Finally, the result is decomposed to obtain parameters of the system elements. The consistency of the proposed estimate is proved and the rate of convergence...

Non-quadratic performance design for Takagi-Sugeno fuzzy systems

Miguel Bernal, Petr Hušek (2005)

International Journal of Applied Mathematics and Computer Science

This paper improves controller synthesis of discrete Takagi-Sugeno fuzzy systems based on non-quadratic Lyapunov functions, making it possible to accomplish various kinds of control performance specifications such as decay rate conditions, requirements on control input and output and disturbance rejection. These extensions can be implemented via linear matrix inequalities, which are numerically solvable with commercially available software. The controller design is illustrated with an example.

Nonquadratic stabilization of continuous-time systems in the Takagi-Sugeno form

Miguel Bernal, Petr Hušek, Vladimír Kučera (2006)

Kybernetika

This paper presents a relaxed scheme for controller synthesis of continuous- time systems in the Takagi-Sugeno form, based on non-quadratic Lyapunov functions and a non-PDC control law. The relaxations here provided allow state and input dependence of the membership functions’ derivatives, as well as independence on initial conditions when input constraints are needed. Moreover, the controller synthesis is attainable via linear matrix inequalities, which are efficiently solved by commercially available...

Nonregular decoupling with stability of two-output systems

Javier Ruiz, Jorge A. Torres Muñoz, Francisco Lizaola (2002)

Kybernetika

In this paper we present a solution to the decoupling problem with stability of linear multivariable systems with 2 outputs, using nonregular static state feedback. The problem is tackled using an algebraic-polynomial approach, and the main idea is to test the conditions for a decoupling compensator with stability to be feedback realizable. It is shown that the problem has a solution if and only if Morse’s list I 2 is greater than or equal to the infinite and unstable structure of the proper and stable...

Normalized finite fractional differences: Computational and accuracy breakthroughs

Rafał Stanisławski, Krzysztof J. Latawiec (2012)

International Journal of Applied Mathematics and Computer Science

This paper presents a series of new results in finite and infinite-memory modeling of discrete-time fractional differences. The introduced normalized finite fractional difference is shown to properly approximate its fractional difference original, in particular in terms of the steady-state properties. A stability analysis is also presented and a recursive computation algorithm is offered for finite fractional differences. A thorough analysis of computational and accuracy aspects is culminated with...

Currently displaying 381 – 400 of 807