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 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.