A further refinement of discretized Lyapunov functional method for the stability of time-delay systems

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

“…As a result of numerical experiment, the system is stable in the region of a corresponding to the negative part of GðA; B; tÞ: The upper bounds of the above example derived from another method are found in the literature [15][16][17]. It is known that the maximum delay to stabilize system (14) is t ¼ 6:1726 according to the analytical results in References [15][16][17], which are obtained via analytic computation.…”

“…It is known that the maximum delay to stabilize system (14) is t ¼ 6:1726 according to the analytical results in References [15][16][17], which are obtained via analytic computation. From Figure 1, the proposed method produces the same maximum stability margin as the existing results.…”

Refined discretized Lyapunov functional method for systems with multiple delays

“…Gu [6] proposed a discretized Lyapunov functional method for such a problem, which is an extension to the single delay case originally proposed in Reference [7]. This paper attempts to simplify the formulation and make the criterion less conservative using the variable elimination technique and Jensen inequality, parallel to the single delay case discussed in Reference [8]. As a result, the stability criterion is significantly simplified.…”

On Computing the Worst-case H∞ Performance of Lur'e Systems with Uncertain Time-invariant Delays

“…Although a bounding technique is not required for this approach, it introduces some slack variables apart from the matrix variables in the LKF. Motivated by [14], Jensen inequality is employed to derive absolute stability criteria for LSTD [7,8]. It is shown in [15] that the FWM approach and Jensen inequality produce the identical results and conservatism, but the latter technique requires less number of decision variables.…”

“…Recently, several researchers proposed novel methods to analyze the absolute stability of LSTD based on the discretization scheme [14,16]. They include delay-decomposition approach [17], -segmentation method [9,12], and delay-dividing approach [10].…”