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Delay-Dependent Stability Criteria for Singular Systems with Interval Time-Varying Delay

DOI: 10.1155/2012/570834

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This paper is concerned with stability analysis for singular systems with interval time-varying delay. By constructing a novel Lyapunov functional combined with reciprocally convex approach and linear matrix inequality (LMI) technique, improved delay-dependent stability criteria for the considered systems to be regular, impulse free, and stable are established. The developed results have advantages over some previous ones as they involve fewer decision variables yet less conservatism. Numerical examples are provided to demonstrate the effectiveness of the proposed stability results. 1. Introduction It is well known that time delays frequently occur in many practical systems, such as biological systems, chemical systems, electronic systems, and network control systems. The time delays are regarded as the major source of oscillation, instability, and poor performance of dynamic systems. During the last two decades, there has been some remarkable theoretical and practical progress in stability, stabilization, and robust control of linear time-delay systems [1, 2]. Currently, the results of stability for time-delay systems mainly focus on time-varying delay with range zero to an upper bound. However, in practice, the delay range may have a nonzero lower bound, and such systems are referred to interval time-varying delay systems. Typical examples for interval time-delay systems are networked control systems [3]. With rapid advancement in the networked control systems technology, a number of significant results have been reported in the recent past for the stability of interval time-delay systems [3–14]. For example, in [3], a discretized Lyapunov functional approach is employed to obtain stability criteria for linear uncertain systems with interval time-varying delays. By using free-weighting matrices, [4, 5] present some less conservative stability conditions. The free-weighting matrices method was further improved in [6, 7] by constructing augmented Lyapunov functionals. The free-weighting matrices method is regarded as an effective way to reduce the conservatism of the stability results; however, one chief shortcoming is that too many free-weighting matrices introduced in the theoretical derivation sometimes cannot reduce the conservatism of the obtained results, on the contrary, they make criteria mathematically complex and computationally less effective. In [8, 9], via different Lyapunov functionals with fewer matrix variables whose derivative is estimated using Jensen inequality, some simple stability criteria were obtained, these results were improved

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