This article is cited in 10 papers

Deterministic Systems

The Lyapunov functions determining the necessary and sufficient conditions for absolute stability of nonlinear nostationary control systems. II

A. P. Molchanov, E. S. Pyatnitskii

Moscow

Abstract: For uniform absolute stability of nonlinear control systems with a range of nonstationary nonlinearities that satisfy sector constraints, the existence of a Lyapunov function from the range of even power forms of a special kind is shown to be necessary and sufficient. This result and the findings of the first installment [1] are extended to the case of a totality of linear nonstationary systems whose coefficients can vary within specified intervals in an unknown way. An example is provided of a nonlinear second-order system in which a Lyapunov function is obtained which specifies the entire region of absolute stability for a parameter which determines the class of nonlinearities.

UDC: 62-501.52


Received: 12.06.1985

 English version: Automation and Remote Control, 1986, 47:4, 445–451

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