Avtomat. i Telemekh., 1988 Issue 5,Pages 178–183(Mi at6688)
Notes
Sufficient conditions for existence of Lyapunov functions from the range of higher power forms in the problem of absolute stability of nonlinear control systems
Abstract:
Nonlinear transformation of the coordinates reduces the design of Lyapunov functions from the range of forms of power $2p$ which establishes absolute stability of a control system with several nonstationary nonlinear elements to analysis of sign definite square form in a cone. Two forms of sufficient conditions for existence of a Lyapunov function from this range are proposed, in the one teh $S$-procedure is used and in the other, the necessary and sufficient conditions for a sign definite square form in a polygonal cone. Examples are provided which demonstrate the improvement of estimates of the range of absolute stability.
Fulltext:
PDF file (725 kB)