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Local asymptotic stability for nonlinear state feedback delay systems

Alfredo Germani, Costanzo Manes, Pierdomenico Pepe (2000)

Kybernetika

This paper considers the problem of output control of nonlinear delay systems by means of state delayed feedback. In previous papers, through the use of a suitable formalism, standard output control problems, such as output regulation, trajectory tracking, disturbance decoupling and model matching, have been solved for a class of nonlinear delay systems. However, in general an output control scheme does not guarantee internal stability of the system. Some results on this issue are presented in this...

Local stability conditions for discrete-time cascade locally recurrent neural networks

Krzysztof Patan (2010)

International Journal of Applied Mathematics and Computer Science

The paper deals with a specific kind of discrete-time recurrent neural network designed with dynamic neuron models. Dynamics are reproduced within each single neuron, hence the network considered is a locally recurrent globally feedforward. A crucial problem with neural networks of the dynamic type is stability as well as stabilization in learning problems. The paper formulates local stability conditions for the analysed class of neural networks using Lyapunov's first method. Moreover, a stabilization...

Mathematical model and optimal control of flow induced vibration of pipelines

N.U. Ahmed (1999)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we consider a dynamic model for flow induced vibration of pipelines. We study the questions of existence and uniqueness of solutions of the system. Considering the flow rate as the control variable, we present three different necessary conditions of optimality. The last one with state constraint involves Differential Inclusions. The paper is concluded with an algorithm for computing the optimal controls.

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...

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...

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.

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...

Observer design for a class of nonlinear discrete-time systems with time-delay

Yali Dong, Jinying Liu, Shengwei Mei (2013)

Kybernetika

The problem of observer design for a class of nonlinear discrete-time systems with time-delay is considered. A new approach of nonlinear observer design is proposed for the class of systems. Based on differential mean value theory, the error dynamic is transformed into linear parameter variable system. By using Lyapunov stability theory and Schur complement lemma, the sufficient conditions expressed in terms of matrix inequalities are obtained to guarantee the observer error converges asymptotically...

On difference linear periodic systems II. Non-homogeneous case

Ion Zaballa, Juan-Miguel Gracia (1985)

Aplikace matematiky

This work deals with the reduction of a linear nonhomogeneous periodic system in differences (recurrence relations) to another linear non-homogeneous system with constant coefficients and an independent term. This makes it possible to study the existence and properties of periodic solutions, the asymptotic behavior and to obtain all solutions in closed form.

On generalized Popov theory for delay systems

Silviu-Iulian Niculescu, Vlad Ionescu, Dan Ivanescu, Luc Dugard, Jean-Michel Dion (2000)

Kybernetika

This paper focuses on the Popov generalized theory for a class of some linear systems including discrete and distributed delays. Sufficient conditions for stabilizing such systems as well as for coerciveness of an appropriate quadratic cost are developed. The obtained results are applied for the design of a memoryless state feedback control law which guarantees the (exponential) closed-loop stability with an ℒ 2 norm bound constraint on disturbance attenuation. Note that the proposed results extend...

Currently displaying 61 – 80 of 150