Extension of Popov's theorems for stability of nonlinear control systems

Abstract

In Part I of this paper, Popov's Theorem PI is first introduced and then a new Theorem I is formulated. The proof is given in Appendix I. An illustrative example shows that the result obtained from Theorem I agrees with that obtained from Lur'e's Theorem. In Part II the linear part transfer function may have poles along the imaginary axis with real positive residues. The nonlinear function f (e) is bounded as well as continuous. Popov's Theorem PII is extended to form a new Theorem II, which gives the condition for quasi-asymptotic stability. Two corollaries are also given. Corollary IIa gives the condition for asymptotic stability. The proof of Theorem II and its corollaries is given in Appendix II. Three examples check with the results of analog computer studies.