By Guang-Ren Duan
Descriptor linear platforms is a vital and wealthy a part of the overall box of keep watch over platforms idea. This e-book presents a scientific improvement of descriptor linear structures protecting elements --- research and layout. The textual content presents thorough introductions to the speculation of continuous-time descriptor linear platforms and to the fundamental effects and up to date advances in descriptor linear platforms conception. Key beneficial properties of study and layout of Descriptor Linear structures: • Introduces real-world examples of descriptor linear structures • offers step by step algorithms for very important research and layout difficulties • Covers either simple and complicated ends up in the literature of continuous-time descriptor linear structures • contains 3 appendices which provide extra proper fabrics helping the content material of pick out chapters within the ebook The transparent presentation of fabrics and large examples make this publication effortless to appreciate by way of a large viewers and accordingly normal readers will locate this publication to be a entire 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 platforms theory.
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Extra info for Analysis and Design of Descriptor Linear Systems
5 Notes and References 29 canonical form, the solution to a general descriptor linear system is further investigated, and the condition for the existence and uniqueness of solution is presented, which actually gives rise to the term of regularity. Chapter 3 further looks at the various properties of regular systems. These include the special equivalent canonical forms, the eigenstructure, the classical and distributional state responses, the stability as well as the transfer functions. As we all know, controllability and observability are a pair of very important concepts for linear systems.
1). 1) is a finite pole of the system. e. forms for descriptor linear systems. These canonical forms all reveal, in a certain sense, the structures of descriptor linear systems, and may have convenient applications in systems analysis and/or design. 7) where x 2 Rn ; u 2 Rr , and y 2 Rm are, respectively, the state vector, the input vector, and the system output vector; E; A 2 RnQ n ; B 2 RnQ r , and C 2 Rm n are constant coefficient matrices. E; A; B; C /. E; A; B/. 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.
Therefore, two equivalent systems must possess certain common properties. Some of the very basic common properties of equivalent systems are also revealed in this section. -R. 1 The Definition For simplicity, let us first make the following conventions: 1. 6) will be omitted in our discussion unless it is necessary to be included. 2. The initial time for the system considered is taken as t0 D 0 unless otherwise specified. 3. 6) is omitted unless when dealing with some problems involving derivative feedback.
Analysis and Design of Descriptor Linear Systems by Guang-Ren Duan