This thesis is devoted to the stability study of timedelay systems, a subject that has been vigorously pursued by such learned societies as diversely represented in mathematics, science, engineering, and economics. Timedelay systems, which are also sometimes known as hereditary systems, systems with memory, after effects and timelag, represent a class of infinitedimensional systems used to describe, among other types of systems, propagation and transport phenomena, population dynamics, economic systems, communication networks, and neural network models. The aim of the present thesis is to develop techniques and tools that may help to study the stability of commensurate timedelay systems. Stability analysis methods are developed based on the corresponding characteristic equation following a frequency sweeping test and constant matrix tests. Rewriting the quasipolynomial equation, the coefficients can be found and then the roots of the characteristic equation can be plotted in a complex plane. If the roots cross the imaginary axis of the system, it is said to be DelayDependent Stable System (DDSS). A controller design procedure for Commensurate Multiple TimeDelay Systems (CMTDSs) is developed, able to transform the system into a Delay Independent Stable System (DISS). The controller based on a single parameter is used to make the system DISS. It may be determined by adopting different strategies, either analytical or graphical. Based on this theorem, a stability chart is partitioned into two regions, that are DDSS and DISS. As an application, it is demonstrated that modelbased design can be used to design systems with time delays. The stability analysis methods developed in this thesis are tailored and applied to find if the system is DDSS and to transform systems from DDSS to DISS.
This thesis is devoted to the stability study of timedelay systems, a subject that has been vigorously pursued by such learned societies as diversely represented in mathematics, science, engineering, and economics. Timedelay systems, which are also sometimes known as hereditary systems, systems with memory, after effects and timelag, represent a class of infinitedimensional systems used to describe, among other types of systems, propagation and transport phenomena, population dynamics, economic systems, communication networks, and neural network models. The aim of the present thesis is to develop techniques and tools that may help to study the stability of commensurate timedelay systems. Stability analysis methods are developed based on the corresponding characteristic equation following a frequency sweeping test and constant matrix tests. Rewriting the quasipolynomial equation, the coefficients can be found and then the roots of the characteristic equation can be plotted in a complex plane. If the roots cross the imaginary axis of the system, it is said to be DelayDependent Stable System (DDSS). A controller design procedure for Commensurate Multiple TimeDelay Systems (CMTDSs) is developed, able to transform the system into a Delay Independent Stable System (DISS). The controller based on a single parameter is used to make the system DISS. It may be determined by adopting different strategies, either analytical or graphical. Based on this theorem, a stability chart is partitioned into two regions, that are DDSS and DISS. As an application, it is demonstrated that modelbased design can be used to design systems with time delays. The stability analysis methods developed in this thesis are tailored and applied to find if the system is DDSS and to transform systems from DDSS to DISS.
New Results on TimeDelay Systems Towards ModelBased Design / Belhamel, Loubna.  (2022 Jan 27).
New Results on TimeDelay Systems Towards ModelBased Design
BELHAMEL, LOUBNA
20220127
Abstract
This thesis is devoted to the stability study of timedelay systems, a subject that has been vigorously pursued by such learned societies as diversely represented in mathematics, science, engineering, and economics. Timedelay systems, which are also sometimes known as hereditary systems, systems with memory, after effects and timelag, represent a class of infinitedimensional systems used to describe, among other types of systems, propagation and transport phenomena, population dynamics, economic systems, communication networks, and neural network models. The aim of the present thesis is to develop techniques and tools that may help to study the stability of commensurate timedelay systems. Stability analysis methods are developed based on the corresponding characteristic equation following a frequency sweeping test and constant matrix tests. Rewriting the quasipolynomial equation, the coefficients can be found and then the roots of the characteristic equation can be plotted in a complex plane. If the roots cross the imaginary axis of the system, it is said to be DelayDependent Stable System (DDSS). A controller design procedure for Commensurate Multiple TimeDelay Systems (CMTDSs) is developed, able to transform the system into a Delay Independent Stable System (DISS). The controller based on a single parameter is used to make the system DISS. It may be determined by adopting different strategies, either analytical or graphical. Based on this theorem, a stability chart is partitioned into two regions, that are DDSS and DISS. As an application, it is demonstrated that modelbased design can be used to design systems with time delays. The stability analysis methods developed in this thesis are tailored and applied to find if the system is DDSS and to transform systems from DDSS to DISS.File  Dimensione  Formato  

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