H_∞ filtering for continuous‐time singular systems with time‐varying delay

Abstract

This paper focuses on H ∞ filter design for continuous-time singular systems with time-varying delay. A delay-dependent H ∞ performance analysis result is first established for error systems via a novel estimation method. By combining a well-known inequality with a delay partition technique, the upper bound of the derivative of the Lyapunov functional is estimated more tightly and expressed as a convex combination with respect to the reciprocal of the delay rather than the delay. Based on the derived H ∞ performance analysis results, a regular and impulse-free H ∞ filter is designed in terms of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the merits of the proposed method.

Exponential H∞ filtering for discrete-time switched singular systems with time-varying delays

“…From [17,33], it is seen that the stability of the filtering error system (3) with wðkÞ ¼ 0 is equivalent to that of system (40).…”

Reliable H ∞ Filtering for Discrete-Time Switched Singular Systems with Time-Varying Delay

“…Compared with state-space models, the study of singular systems is more arduous, since not only stability, but also regularity and impulse elimination (for continuous-time singular systems) and causality (for discrete-time singular systems) should be considered simultaneously, while the latter two do not appear in state-space ones [37]. Recently, much appreciable work has been performed on the design of H ∞ filters for many kinds of singular system in various settings, including systems with or without time delay [11,14,21,36,39,41,43,45], systems with stochastic switching [22,35], and discrete-time switched systems under arbitrary switching signals [13]. However, to the authors' knowledge, the problem of H ∞ filter design for discrete-time switched singular time-delay systems has not been fully studied.…”

Fault detection for singular multiple time-delay systems with application to electrical circuit

“…Then the FD scheme in these existing results can be stated as follows: Z þ1 whererðtÞ ¼ rðtÞÀf ðtÞ. Moreover, via the Lyapunov function approaches given in [12,19,20], one can obtain the corresponding FD filter design conditions. It should be pointed out that, by using the method of [2], the weighting matrices in Eq.…”

“…Just as pointed out in [6], singular systems provide a more general representation than standard state-space systems in the sense of modeling. Many fundamental system theories developed for state-space systems have been successfully generalized to their counterparts for singular systems, for example, controllability and observability [7], filter design [8][9][10][11][12], observer design [13], stability analysis [14,15] and fault tolerant control [16,17], etc. Especially, the fault detection problems for singular systems have been studied in [18][19][20][21][22][23].…”