Stability boundaries of mechanical controlled system with time delay

The problem of determining critical time delays where an actively controlled mechanical system may loss or gain stability is considered. It is shown that for the Single-Input–Multiple-Output controlled system the problem may be reduced by using Singular Value Decomposition to a problem of finding the roots of a certain polynomial. The technique cannot be extended to the Multiple-Input–Multiple-Output controlled system. Two numerical methods are developed to solve this case. One involved Newton's iterations and the other involves Bisection for multiple functions.

► Active control includes time delay between state sensing and control actuation. ► Time delay may destabilize the system. ► Numerical algorithms for finding critical time delay are developed. ► The theory of time delay stabilization is obtained from first principles.