From Exponential to Polynomial Complexity in the Lyapunov Stability Test

By the Lyapunov Stability Test, we refer to a previously developed criterion for the exponential stability of linear time-invariant delay systems. This criterion requires the validation of a special matrix, expressed in terms of a discrete set of values of the delay Lyapunov matrix, for positive definiteness. The dimension of this matrix is determined by the system parameters and deduced from some conservative estimates. In this paper, we have significantly reduced the conservatism. As a result, we obtained a dimension that depends cubically on the delay value, whereas previously this dependence was exponential. Copyright (c) 2024 The Authors.