Robust observer‐based control design for uncertain singular systems with time‐delay

Abstract

SUMMARYThis paper is concerned with the stability analysis and robust dynamic output feedback controller synthesis for uncertain continuous singular systems with time‐delay. First, on the basis of the Lyapunov functional method and by resorting to the delay‐partition technique, improved delay‐dependent sufficient conditions are presented to ensure the nominal unforced system to be admissible (i.e., to be regular, impulse‐free, and stable). Second, with the help of the obtained admissibility criterion, an observer‐based controller is designed by solving a set of LMIs. Finally, the validity and applicability of the proposed approach is shown by examples. Copyright © 2013 John Wiley & Sons, Ltd.

Robust Stability Analysis of Takagi–Sugeno Fuzzy Nonlinear Singular Systems with Time-Varying Delays Using Delay Decomposition Approach

“…Thus, from (19) and (21), we conclude that the system (2) is asymptotically stable. According to Definition 1, we conclude that the system (2) is admissible.…”

“…In Table 1, 'm' denotes the delay-partitioning number. From Table 1, it is clear that the stability criterion proposed in Corollary 2 yields much less conservative results than the results [10][11][12][13]19,38] in the existing literature.…”

“…In corollary 2, the delay-dependent stability conditions are derived by choosing proper LKF, which yields less conservative results than the existing results obtained in [10][11][12][13]19,38]. Here, the tuning parameter α plays an important role in the reduction in conservatism.…”

“…In fact, singular systems can be found in many applications such as electrical circuits, economic systems, moving robots and many other systems, because they can better describe physical systems than state-space systems, for details (see [2,[10][11][12][13]19,[37][38][39]). It should be pointed out that the stability problem of singular systems is much more complicated than state-space systems, because it requires considering not only stability, but also it required regularity and impulse-free conditions (for continuous systems).…”

Observer-basedH∞control for uncertain singular time-delay systems with actuator saturation

“…By comparing the stability criterion of Theorem 1 with that of [16,25,26] for the preceding system, we have Table I. Hence, for this example, the stability criterion we derived is less conservative than that reported in the aforementioned papers.…”