Stability and Stabilization

Daizhan Cheng (), Xiaoming Hu () and Tielong Shen ()
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Daizhan Cheng: Chinese Academy of Sciences, Academy of Mathematics & Systems Science
Xiaoming Hu: Royal Institute of Technology, Optimization and Systems Theory
Tielong Shen: Sophia University, Department of Engineering and Applied Sciences

Chapter Chapter 7 in Analysis and Design of Nonlinear Control Systems, 2010, pp 173-206 from Springer

Abstract: Abstract 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 first priority to be consider. This chapter considers the stability of dynamic systems and the stabilization and stabilizer design of nonlinear control systems. In Section 7.1 the concepts about stability of dynamic systems are presented. Section 7.2 considers the stability of nonlinear systems via its linear approximation. The Lapunov direct method is discussed in Section 7.3. Section 7.4 presents the LaSalle’s invariance principle. The converse theory of Lyapunov stability is introduced in Section 7.5. Section 7.6 is about the invariant set. The input-output stability of control systems is discussed in Section 7.7. In section 7.8 the semi-tensor product is used to find the region of attraction. Many results in this chapter are classical, hence the proofs are omitted.

Keywords: Equilibrium Point; Exponential Stability; Nonlinear Control System; Floquet Multiplier; Unstable Eigenvalue (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-11550-9_7

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DOI: 10.1007/978-3-642-11550-9_7

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