Tomáš Vyhlídal

An eigenvalue based approach for the stabilization of linear time-delay systems of neutral type

An eigenvalue based approach for the stabilization of linear neutral functional differential equations is presented, which extends the recently developed continuous pole placement method for delay equations of retarded type. The approach consists of two steps. First the stability of the associated difference equation is determined and a procedure is applied to compute the supremum of the real parts of its characteristic roots, which corresponds to computing the radius of the essential spectrum of the solution operator of the neutral equation. No restrictions are made on the dimension of the system and the number of delays. Also the effect of small delay perturbations is explicitly taken into account. As a result of this first step the stabilization problem of the neutral equation is reduced to a problem involving only a finite number of characteristic roots. As a second step, stabilization is achieved by shifting the rightmost or unstable characteristic roots to the left half plane in a quasi-continuous way, by applying small changes to the controller parameters, and meanwhile monitoring other characteristic roots with a large real part. A numerical example is presented.

Quasipolynomial mapping based rootfinder for analysis of time delay systems

Abstract An original method for computing poles and zeros of time delay systems based on mapping the characteristic functions (quasipolynomials) of the system is presented. The method, which locates all the quasipolynomial roots in a bounded region, is based on mapping the real and imaginary parts of the quasipolynomial in the complex plane using the level curve tracing algorithm.

QPmR - Quasi-Polynomial Root-Finder: Algorithm Update and Examples

An updated QPmR algorithm implementation for computation and analysis of the spectrum of quasi-polynomials is presented. The objective is to compute all the zeros of a quasi-polynomial located in a given region of the complex plane. The root-finding task is based on mapping the quasi-polynomial in the complex plane. Consequently, utilizing spectrum distribution diagram of the quasi-polynomial, the asymptotic exponentials of the retarded chains are determined. If the quasi-polynomial is of neutral type, the spectrum of associated exponential polynomial is assessed, supplemented by determining the safe upper bound of its spectrum. Next to the outline of the computational tools involved in QPmR, its Matlab implementation is presented. Finally, the algorithm is demonstrated by three examples.

Time Delay Systems: Methods, Applications and New Trends

This volume is concerned with the control and dynamics of time delay systems; a research field with at least six-decade long history that has been very active especially in the past two decades. In parallel to the new challenges emerging from engineering, physics, mathematics, and economics, the volume covers several new directions including topology induced stability, large-scale interconnected systems, roles of networks in stability, and new trends in predictor-based control and consensus dynamics. The associated applications/problems are described by highly complex models, and require solving inverse problems as well as the development of new theories, mathematical tools, numerically-tractable algorithms for real-time control. The volume, which is targeted to present these developments in this rapidly evolving field, captures a careful selection of the most recent papers contributed by experts and collected under five parts: (i) Methodology: From Retarded to Neutral Continuous Delay Models, (ii) Systems, Signals and Applications, (iii): Numerical Methods, (iv) Predictor-based Control and Compensation, and (v) Networked Control Systems and Multi-agent Systems.

Signal shaper with a distributed delay: Spectral analysis and design

Input shapers with time delays have proved useful in many applications related to controls for various oscillatory devices, for example flexible manipulators and cranes. In the paper, a novel approach for designing a zero-vibration signal shaper based on equally distributed delay is proposed. The parameter assessment of the shaper is based on the spectral approach. Various characteristics of the shaper are analyzed and compared with the classical zero-vibration shaper with a lumped delay. The analysis shows that the novel shaper is a slower, but more robust alternative to the classical shaper. Besides, the discrete implementation of the shaper is proposed and tested. It includes zero placement based parameter adjustment with the objective to preserve full compensation of the oscillatory mode by the discrete algorithm.

Strong Stability of Neutral Equations with an Arbitrary Delay Dependency Structure

The stability theory for linear neutral equations subjected to delay perturbations is addressed. It is assumed that the delays cannot necessarily vary independently of each other, but depend on a possibly smaller number of independent parameters. As a main result, necessary and sufficient conditions for strong stability are derived along with bounds on the spectrum, which take into account the precise dependency structure of the delays. In the derivation of the stability theory, results from realization theory and determinantal representations of multivariable polynomials play an important role. The observations and results obtained in the paper are first illustrated and validated with a numerical example. Next, the effects of small feedback delays on the stability of a boundary controlled hyperbolic partial differential equation and of a control system involving state derivative feedback are analyzed.

Stabilizability and Stability Robustness of State Derivative Feedback Controllers

We study the stabilizability of a linear controllable system using state derivative feedback control. As a special feature the stabilized system may be fragile, in the sense that arbitrarily small modeling and implementation errors may destroy the asymptotic stability. First, we discuss the pole placement problem and illustrate the fragility of stability with examples of a different nature. We also define a notion of stability, called

Climate for Culture: assessing the impact of climate change on the future indoor climate in historic buildings using simulations

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Parameterization of input shapers with delays of various distribution

-stability, which explicitly takes into account the effect of small modeling and implementation errors. Next, we investigate the effect on the fragility of including a low-pass filter in the control loop. Finally, we completely characterize the stabilizability and

Zero vibration shapers with distributed delays of various types

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