Analysis and Design of Descriptor Linear Systems by Guang-Ren Duan

By Guang-Ren Duan

Descriptor linear platforms is a crucial and wealthy a part of the final box of regulate structures conception. This e-book offers a scientific improvement of descriptor linear platforms overlaying elements --- research and layout. The textual content presents thorough introductions to the idea of continuous-time descriptor linear platforms and to the elemental effects and up to date advances in descriptor linear structures conception. Key positive aspects of research and layout of Descriptor Linear platforms: • Introduces real-world examples of descriptor linear structures • offers step by step algorithms for vital research and layout difficulties • Covers either simple and complicated ends up in the literature of continuous-time descriptor linear platforms • comprises 3 appendices which provide extra suitable fabrics assisting the content material of decide upon chapters within the booklet The transparent presentation of fabrics and huge examples make this publication effortless to appreciate via a large viewers and consequently common readers will locate this ebook to be a complete creation to the speculation of descriptor linear platforms. Researchers will discover a complete description of the latest ends up in this thought and scholars will discover a strong advent and assessment to a few very important difficulties in linear structures theory.

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The problem is to present conditions for the existence of a certain type of controllers for a descriptor linear system, such that the closed-loop system is regular. The types of controllers involved are basically those static linear feedback ones discussed in Sect. 1. Stability Stability of a dynamical system describes the response behavior of the system at infinity with respect to initial condition disturbances, and is well regarded as one of the most important properties of dynamical systems.

1 Dynamics Decomposition Form Now let us introduce the so-called dynamics decomposition form, which is the most basic restricted equivalent form for descriptor linear systems. 8) EQ D QEP D n0 0 0 This immediately suggests the following result. 2. 8). 7). Since this canonical form clearly separates the dynamical part (represented by the dynamical state equation) and the static part (represented by the algebraic equation), it is called the dynamics decomposition form. 9) reveals the physical structure of descriptor linear systems.

This includes the finite and infinite poles of the two systems, the transfer functions, and the different types of controllability and observability of the system, etc. 3 Problems for Descriptor Linear Systems Analysis and Design 23 Finding for a certain type of descriptor linear systems some equivalent canonical forms, which offer easy understandings about this type of systems and provide convenience for analysis and control of this type of systems. Normalizability As we have found out in Sect.

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