Wyniki wyszukiwania - BazTech

1

The revision and extension of the RMS ring for time delay systems

Pekař L., Prokop R.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2017

|

Vol. 65, nr 3

341--349

EN

This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (RMS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.a. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMS simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions RQM is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.

2

Robust stability of positive linear time delay systems under time-varying perturbations

Ngoc P. H. A., Tinh C. T.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2015

|

Vol. 63, nr 4

947--954

EN

By a novel approach, we get explicit robust stability bounds for positive linear time-invariant time delay differential systems subject to time-varying structured perturbations or non-linear time-varying perturbations. Some examples are given to illustrate the obtained results. To the best of our knowledge, the results of this paper are new.

3

A Lyapunov functional for a system with a time-varying delay

Duda J.

International Journal of Applied Mathematics and Computer Science

|

2012

|

Vol. 22, no. 2

327-337

EN

The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval time-varying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

4

Delay-dependent Asymptotic Stabilitzation for Uncertain Time-delay Systems with Saturating Actuators

Liu P. L.

International Journal of Applied Mathematics and Computer Science

|

2005

|

Vol. 15, no 1

45-51

EN

This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.

5

Szego's First Limit Theorem in Terms of a Realization of a Continuous-Time Time-Varying System

Iglesias P. A., Zang G.

International Journal of Applied Mathematics and Computer Science

|

2001

|

Vol. 11, no 6

1261-1276

EN

It is shown that the limit in an abstract version of Szego's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.

6

Motion Planning, Equivalence, Infinite Dimensional Systems

Rouchon P.

International Journal of Applied Mathematics and Computer Science

|

2001

|

Vol. 11, no 1

165-188

EN

Motion planning, i.e., steering a system from one state to another, is a basic question in automatic control. For a certain class of systems described by ordinary differential equations and called flat systems (Fliess et al., 1995; 1999a), motion planning admits simple and explicit solutions. This stems from an explicit description of the trajectories by an arbitrary time function y, the flat output, and a finite number of its time derivatives. Such explicit descriptions are related to old problems on Monge equations and equivalence investigated by Hilbert and Cartan. The study of several examples (the car with n-trailers and the non-holonomic snake, pendulums in series and the heavy chain, the heat equation and the Euler-Bernoulli flexible beam) indicates that the notion of flatness and its underlying explicit description can be extended to infinite-dimensional systems. As in the finite-dimensional case, this property yields simple motion planning algorithms via operators of compact support. For the non-holonomic snake, such operators involve non-linear delays. For the heavy chain, they are defined via distributed delays. For heat and Euler-Bernoulli systems, their supports are reduced to a point and their definition domain coincides with the set of Gevrey functions of order 2.

7

A Problem of Robust Control of a System With Time Delay

Blizorukova M., Kappel F., Maksimov V.

International Journal of Applied Mathematics and Computer Science

|

2001

|

Vol. 11, no 4

821-834

EN

A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part' of coordinates) is designed. The algorithm is stable with respect to informational noises and computational errors.

8

Robust Dynamic Input Reconstruction for Delay Systems

Kappel F., Maksimov V.

International Journal of Applied Mathematics and Computer Science

|

2000

|

Vol. 10, no 2

283-307

EN

A problem of reconstruction of a non-observable control input for a system with a time delay is analyzed within the framework of the dynamical input reconstruction approach (see Kryazhimskii and Osipov, 1987; Osipov and Kryazhimskii, 1995; Osipov et al., 1991). In (Maksimov, 1987; 1988) methods of dynamical input reconstruction were described for delay systems with fully observable states. The present paper provides an input reconstruction algorithm for partially observable systems. The algorithm is robust to the observation perturbations.

9

Robust Stabilization for Uncertain Time-Varying Delay Constrained Systems With Delay-Dependence

Han Q. L., Mehdi D.

International Journal of Applied Mathematics and Computer Science

|

1999

|

Vol. 9, no 2

293-311

EN

This paper is concerned with the problem of robust stabilization of linear time-varying delay systems containing saturating actuators in the presence of nonlinear parametric perturbations. Based on Razumikhin's approach to the stability of functional differential equations, we determine upper bounds on the time-varying delay such that the uncertain system under consideration is robustly globally or locally asymptotically stabilizable via memoryless state feedback control laws. The obtained bounds are given in terms of solutions to Lyapunov equations. Two numerical examples are included to illustrate the results.

10

Detection and Regulation Problems for Discrete-Time Distributed Systems With Delays

Namir A., Lahmidi F., Alif O.

International Journal of Applied Mathematics and Computer Science

|

1999

|

Vol. 9, no 2

347-369

EN

A distributed discrete-time hereditary system is considered. An unknown input is supposed to be a perturbation. First, we investigate the possibility of reconstructing this input using the information provided by an output equation. Then we treat the problem of keeping the observation as close as possible to some desired values (with the system still perturbed by the unknown input). To illustrate the results, some examples are presented.