H∞ control of singular time-delay systems via discretized Lyapunov functional

Robust H∞ Control For Uncertain Singular Neutral Time-Delay Systems

“…Hence, the effect of disturbances on the considered systems should be taken into account. Since H ∞ control is used to keep systems less sensitive to disturbances, problems of H ∞ control for time-delay systems have been widely explored, and findings related to these problems have been reported many times in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] as a result of their frequent applications in power systems, large-scale systems, and circuit systems. Recently, scholars (such as [11][12][13][14][15]) have started to study the H ∞ problem for singular time-delay systems by using a linear matrix inequality (LMI) approach, which yields not only the existence conditions valid for singular systems' regular problems but also characterizations of H ∞ controllers, leading to a convex optimization problem [16][17][18][19][20][21][22][23][24][25][26][27][28][29].…”

RobustH∞Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach

“…It is well-known that Lyapunov-Krasovskii theorems are basic theories for the study of all types of time-delay system [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. The choice of appropriate Lyapunov-Krasovskii functional (LKF) is crucial for obtaining stability criteria and bounded real lemmas (BRLs) and, as a result, for obtaining solutions to various control problems.…”

“…On the other hand, LMI stability conditions via complete quadratic LKF and discretization were introduced by Gu in [17] for time delay system and appeared to be very efficient, leading in some examples to results close to analytical ones. The discretized LKF method has been extended to singular time-delay systems in [16]. An improved bounded real lemma (BRL) is presented by discretization LKF method which greatly lowers the conservatism, but the initial parameter is needed to introduce controller design.…”

Robust Observer and Observer‐Based Controller for Time‐Delay Singular Systems

“…Many types of controllers are considered, observer-based controller [16], state feedback controller [12,14], and dynamic output feedback controller. To avoid the first reason, [17] presented a singular-type complete quadratic LKF combined with the discretization LKF method to obtain a new BRL. To avoid the first reason, [17] presented a singular-type complete quadratic LKF combined with the discretization LKF method to obtain a new BRL.…”