Robust stability analysis for uncertain delay systems with output feedback controller

Robustness of exponential stability of stochastic differential delay equations

“…when g = 0, such problem has been studied recently by several authors e.g. Hale [1], Mori and Kokame [8,9], Su, Fong, Tseng [10][11][12]. This paper is to extend their results to the stochastic case but the mathematical techniques employed here are very much different from theirs.…”

“…It should also be pointed out that Su, Fong and Tseng [10][11][12] recently obtained several alternative criteria for the asymptotic stability of equations (4.1) and (4.2). For example, Su [10] obtained the following result: Equation (4.2) is asymptotic stability if…”

Stability robustness of linear output feedback systems with both time-varying structured and unstructured parameter uncertainties as well as delayed perturbations

“…Applying those previous robust stability analysis results [1][2][3][4][5][6][7][8] to solve this problem is not easy, in that after output feedback, there will be coupled terms of parameters in the closedloop system matrix because of the uncertain parameters in both input and output matrices [9]. Though we may regard these coupled terms as new independent parameters if we insist on using previous robust stability analysis results, Su and Fong [9] and Tseng et al [10] have showed that a conservative analysis conclusion may be reached. Therefore, Tseng et al [10] applied the structured singular value technique to solve the robust stability problem of linear state delayed systems with constant output feedback in the presence of time-varying uncertain parameters by directly considering the coupled terms in the problem formulation.…”

Exponential stability of nonlinear delay equation with constant decay rate via perturbed system method

“…Perturbed system method, which regards the considered delay system as the perturbed system of the corresponding crisp system (without delay), has been used to analyze stability of delay systems (see, e.g., [2,3] where the delay-independent conditions have been proposed; and [3][4][5][6][7] where the authors presented several delay-dependent results). In the direction of this method, Mao [8] with its modified version [9] investigated the exponential stability of general nonlinear delay systems of the form…”

“…Recently, a great number of stability results have been proposed using various methods (see, e.g., [1][2][3][4][5][6][7][8], and the cited references therein). Noting that there exist two notions concerning stability of a delay system, namely, delay dependence and delay independence.…”