Stability Criteria for Second-Order Dynamical Systems With Time Lag

[+] Author and Article Information
S. J. Bhatt

The Boeing Company, Renton, Wash.

C. S. Hsu

Division of Applied Mechanics, University of California, Berkeley, Calif.

J. Appl. Mech 33(1), 113-118 (Mar 01, 1966) (6 pages) doi:10.1115/1.3624967 History: Received February 16, 1965; Online September 15, 2011


Stability of second-order dynamical systems with time lag is investigated by using Pontrjagin’s theorems on the zeros of exponential polynomials. The time-lag term may involve the displacement, the velocity, or the acceleration. Systems with negative damping coefficient and/or negative spring constants are also considered. It is shown that a delayed feedback signal of proper strength and proper delay is capable of stabilizing such dynamical systems with negative damping and/or negative spring constants. It is also found that some earlier results given in [2] for the restricted case where the damping coefficient is positive and the spring constant is non-negative are defective. The stability criteria obtained here are expressed in terms of inequalities which impose upper and lower bounds for the system parameters.

Copyright © 1966 by ASME
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