Class Of Delay Systems Research Articles

Stability criteria of arbitrary-order neutral dynamic systems with mixed delays

The stability of a neutral dynamic system is a major study in the class of delay systems. In this effort, we study the stability of fractional-order nonlinear dynamic systems utilizing Lyapunov direct method based on fractional calculus (fractional differential operator and fractional integral operator type Riemann–Liouville operators). We suggest a new non-Lipschitz fractional Lyapunov function. This function is a generalization of the well known Lyapunov functions. We investigate the speed of convergence for special cases. Applications are clarified in the sequel.

Stability conditions for time delay systems in terms of the Lyapunov matrix

An overview of stability conditions in terms of the Lyapunov matrix for time-delay systems is presented. The main results and proof strategies are outlined in the retarded type case. The state of the art and potential extensions to other classes of delay systems are discussed.

Robust Absolute Stabilization of Time-Varying Delay Systems with Maximum Admissible Perturbed Bound

This paper is concerned the problem of robust absolute stabilization of time-varying delay systems with admissible perturbation in terms of integral inequality. A linear state-feedback control law is derived for one class of delay systems with sector restriction based on linear matrix inequality (LMI). Especially, this method does not require input terms are absolutely controllable for nonlinear delay systems. Numerical example is used to demonstrate the validity of the proposed method.

Stability analysis and controller design for a class of delay systems via observer based on network

This paper focuses on the problem of stability analysis and controller design for a class of delay systems based on networked control systems. By introducing some free matrix variables, some criteria for stability analysis and observer-based control law design can be obtained by the solving of linear matrix inequalities. A numerical example is also offered to prove the effectiveness of the proposed method.

Real-time calculation of the current state estimates for a class of delay systems

The linear optimal observation problem is examined for one type of nonstationary delay system with an uncertainty in the initial state. A fast implementation of the dual method is proposed for calculating estimates of the initial state. This implementation is based on the quasi-reduction of the fundamental matrix of solutions to the mathematical model of delay systems. It is shown that an iteration step of the dual method only requires that auxiliary systems of ordinary differential equations be integrated on small time intervals. An algorithm is described for the real-time calculation of current state estimates. The results are illustrated by the optimal observation problem for a third-order stationary delay system.

NUMERICAL COMPUTATION OF CHARACTERISTIC MULTIPLIERS FOR LINEAR TIME PERIODIC COEFFICIENTS DELAY DIFFERENTIAL EQUATIONS

in this work we address the question of asymptotic stability of linear delay differential equations (DDEs) with time periodic coefficients, a class which is recognized to be fundamental in machining tool.Since the dynamics of such a class of delay systems is governed by the dominant eigenvalues (multipliers) of the monodromy operator associated to the system of DDEs, i.e. the solution operator over the period of the coefficients, we discretize it by using pseudospectral differencing techniques based on collocation and approximate the dominant multipliers by the eigenvalues of the resulting matrix. The use of pseudospectral methods has already been proposed in the context of simpler DDEs. Here we fully generalize the method to the class of linear time periodic coefficients DDEs with arbitrary period and multiple discrete and distributed delays.The scheme is shown to have spectral accuracy by means of several numerical examples.

Uniform asymptotic stability of hybrid dynamical systems with delay

We formulate a model for hybrid dynamical systems with delay, which covers a large class of delay systems. Under several mild assumptions, we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via a Lyapunov-Razumikhin technique. To demonstrate the developed theory, we conduct stability analyses for delay sampled-data feedback control systems including a nonlinear continuous-time plant and a linear discrete-time controller.

Laguerre and Kautz shift approximations of delay systems

Certain Laguerre and Kautz shift-induced, finite-dimensional approximations of an important class of delay systems are studied. A substantially complete set of lower and upper H infinity and H2/L2 error bounds is given. Furthermore, exact asymptotic H infinity error formulas are provided. The Laguerre formula provides surprisingly good finite-dimensional models of delay systems in the most transparent manner possible.

Stabilization of a class of linear delay systems

A form of stabilizing feedback law is proposed for a class of delay systems occurring frequently in practice. It makes use of predictor forms elaborated with distributed delays. Two examples are examined and a procedure for single-input, single-output systems is given. A comparison with other schemes leading to finite spectrum assignment is then outlined.

Feedback stabilization of neutral systems via the transformation technique

Within the class of delay systems, a neutral system may be distinguished by the possible presence of a neutral root chain—an infinite chain of eigenvalues in a vertical strip of the complex plane. Assuming that such a neutral root chain, if it exists, is stable, this work shows how our method of transformation can be extended to obtain feedback controllers for this class of neutral systems.

Model reduction of delay systems using Pade approximants

This paper describes the rational approximation of a certain class of delay systems in the frequency domain using Pad£ approximants of exp(−sT). Three classes of approximants characterized by their relative degrees are considered. Easily computable a priori L∞ and L L2error bounds are provided.

Analysis of time-varying delay systems via general orthogonal polynomials

General orthogonal polynomials are introduced in order to analyse and approximate the solution of a class of delay systems. Using the operational matrix of integration, together with the operational matrix of linear transformation, the dynamical equation of a delay system is reduced to a set of simultaneous linear algebraic equations. The coefficient vectors of the general orthogonal polynomials can be determined recursively by use of the derived algorithm. Examples are given to demonstrate the validity and applicability of the orthogonal-polynomial approximations.