Constrained simulated annealing for stability margin computation in a time‐delay system

Abstract

SUMMARYThe stability margin of a time-delay system is formulated via factorization. This paper provides a numerical method for computing the stability margin of time-delay linear time-invariant systems with delay dependence by using a constrained simulated annealing algorithm. The constrained simulated annealing is used to solve a nonlinear continuous constrained optimization problem, which is derived from computing the stability margin of a delay system. Illustrative examples show that the established method can verify the stability for a class of time-delay systems.

Estimating the delay margin for stability of linear delay systems by the weighted matrix measure

“…Notably, some of these approaches can compute the exact delay margin without any additional conservatism. 18,19,22 Most of the mentioned works for the delay margin problems are concerned with single-delay systems. To our knowledge, studies on delay margin problem of linear systems with multiple incommensurate delays are scarce.…”

“…Matrix measure approaches for the delay margin estimation are studied in References 15‐17. In Reference 18, by using the factorization of transfer function the exact delay margin problem is changed into a constrained nonlinear optimization problem. Using Padé approximations for the function $$$ \exp \left(-s\right) $$$, Reference 19 presents a comparison system approach to reduce the conservatism of delay margin.…”

“…The frequency‐domain approaches are effective in dealing with single delay cases. Notably, some of these approaches can compute the exact delay margin without any additional conservatism 18,19,22 …”