Admissibility Analysis of a Sampled‐Data Singular System Based on the Input Delay Approach

Abstract

This study investigates the sampled-data admissibility problem for a singular system. The objective of this paper is to design a sampled-data controller to ensure the admissibility of a singular system and to construct an appropriate Lyapunov–Krasovskii functional (LKF) to get less conservative results for the sampled-data singular system. To accomplish these objectives, the system is converted into a time-delay system by the input delay approach firstly, and both lower and upper bounds of the delay are considered. Secondly, by introducing a suitable LKF, the admissibility criteria are obtained. Then, when estimating the derivative of the LKF, a relaxation variable is introduced by the method of reciprocally convex inequality, and it is proved that the conservatism is reduced. Finally, two numerical examples are given to prove that the designed sampled-data controller can ensure the states of the systems under the influence of external interference.

Sampled-Data Control for a Class of Singular Takagi-Sugeno Fuzzy Systems with Application in Truck-Trailer System

“…Remark 1. If E = I, then system ( 7) is simplified to a normal fuzzy system, and the sampleddata control problem is discussed in [42][43][44]. However, in [42], the lower bound of the sampling period is assumed to be zero, which limits its application range and leads to conservatism in the results.…”

“…In [43], the constant sampling periods are considered, but the variable sampling periods are omitted. In [44], the admissible issue for a sampled-data singular system is discussed. However, this method is only suitable for linear-singular systems.…”

“…In the paper, the sampled-data control issue for nonlinear-singular systems is discussed, and both the lower and upper bounds of the sampling period are considered. If d 1 = d 2 = d, then the sampling period will become a constant, as it is in [42][43][44]. Therefore, the proposed methods have a wider range of applications than these references.…”

Mathematical Model for Fault Handling of Singular Nonlinear Time-Varying Delay Systems Based on T-S Fuzzy Model

“…Singular systems, also known as generalized systems, are more complex systems than general systems, consisting of faster-changing differential systems and slower-changing algebraic equations [1][2][3]. There are still many unsolved problems waiting to be studied, and the study of singular systems is very meaningful.…”