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17 Result(s)
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Book
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Chapter
Topological Space
The purpose of this chapter is to present some basic topological concepts of point sets. What we discuss here is very elementary, thus should not be considered as a comprehensive introduction to topology. But ...
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Chapter
Decoupling
Section 8.1 considers the (f, g)-invariant distribution of a nonlinear system. Quaker lemma is proved, which assures the equivalence between two kinds of (f, g)- invariances. Quaker lemma is the foundation of the...
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Chapter
Output Regulation
Output regulation is the problem of finding a control law by which the output of the concerning plant can asymptotically track a prescribed trajectories and/or asymptotically reject undesired disturbances. Mea...
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Chapter
Controllability and Observability
In section 5.1 we consider controllability of nonlinear systems. The materials are mainly based on [11, 10]. We also refer to [5, 9] for related results, to [4] for later developments. Section 5.2 is about obs...
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Chapter
Dissipative Systems
This chapter discusses the dissipative systems. First, the definition and the properties of two kinds of dissipative systems, mainly passive system and γ-dissipative system, are introduced in Section 13.1. The...
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Chapter
Algebra, Lie Group and Lie Algebra
Geometry, algebra, and analysis are usually called the three main branches of mathematics. This chapter introduces some fundamental results in algebra that are mostly useful in systems and control. In section ...
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Chapter
Global Controllability of Affine Control Systems
This chapter investigates global controllability of general affine control systems, including linear and nonlinear, switched and non-switched ones. The main purpose is to establish criteria for the controllabi...
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Chapter
Linearization of Nonlinear Systems
Linearization is one of the most powerful tools for dealing with nonlinear systems. Some person says that in fact, what the mathematicians can really deal with is linear problems. Believe it or not, the contro...
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Chapter
L 2 -Gain Synthesis
This chapter investigates L2-gain synthesis problem. As L2-induced norm, L2-gain is an extension of H ∞ norm of linear systems. Hence, L2-gain synthesis problem is usually ...
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Chapter
Discontinuous Dynamical Systems
This chapter discusses analysis and design problems of discontinuous dynamic systems represented by differential equations with discontinuous right-hand side. After a brief review of discontinuous dynamic syst...
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Chapter
Introduction
In this chapter we give an introduction to control theory and nonlinear control systems. In Section 1.1 we briefly review some basic concepts and results for linear control systems. Section 1.2 describes some ...
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Chapter
Differentiable Manifold
This chapter provides an outline of Differential Geometry. First we describe the fundamental structure of a differentiable manifold and some related basic concepts, including map**s between manifolds, smooth...
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Chapter
Stability and Stabilization
Stability is a fundamental property for dynamic systems. In most engineering projects unstable systems are useless. Therefore in system analysis and control design the stability and stabilization become the fi...
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Chapter
Design of Center Manifold
This chapter provides a systematic technique for designing center manifold of closed loop of nonlinear systems to stabilize the system. The method was firstly presented in [6]. Section 11.1 introduces some fun...
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Chapter
Input-Output Structure
This chapter considers the structure of an affine nonlinear systems from a viewpoint of the relation between inputs and outputs. Section 9.1 considers the relative degree and the decoupling matrix. Section 9.2...
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Chapter
Switched Systems
As the simplest hybrid system a switched system has many industrial backgrounds and engineering applications. Theoretically, it is also challenging: Switching adds complexity, and at the same time provides mor...
