Reliable filtering for discrete time-delay systems with randomly occurred nonlinearities via delay-partitioning method

Abstract

In this paper, the reliable H ∞ filtering problem is investigated for a class of uncertain discrete time-delay systems with randomly occurred nonlinearities (RONs) and sensor failures. RONs are introduced to model a class of sectorlike nonlinearities that occur in a probabilistic way according to a Bernoulli distributed white sequence with a known conditional probability. The failures of sensors are quantified by a variable varying in a given interval. The time-varying delay is unknown with given lower and upper bounds. The aim of the addressed reliable H ∞ filtering problem is to design a filter such that, for all possible sensor failures, RONs, time-delays as well as admissible parameter uncertainties, the filtering error dynamics is asymptotically mean-square stable and also achieves a prescribed H ∞ performance level. Sufficient conditions for the existence of such a filter are obtained by using a new Lyapunov-Krasovskii functional and delay-partitioning technique. The filter gains are characterized in terms of the solution to a set of linear matrix inequalities (LMIs). A numerical example is given to demonstrate the effectiveness of the proposed design approach.

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

“…, −1, 0 is a given initial condition sequence. In this paper, the following sensor failure model, as introduced in [20], is adopted to describe the measured signal sent from the sensors:…”

“…In the past few years, a number of reliable filtering results have been presented; see, e.g. [7,20,27,32,40]. Unfortunately, up to now, the problem of reliable H ∞ filtering for discrete-time switched singular time-delay systems, even for non-switched systems, remains open and unsolved.…”

Reliable finite-time H ∞ filtering for discrete time-delay systems with Markovian jump and randomly occurring nonlinearities

“…The delay partitioning technique has been widely used to deal with time-delay systems that has shown the potential of reducing conservatism, see [27]. To reduce conservativeness of stability criteria of stochastic system with time delays, we adopt delay partitioning technique and the slack matrix approach in this paper.…”

“…Such nonlinear disturbances may occur in a probabilistic way and are randomly changeable in terms of their types or intensity, which are then named as randomly occurring nonlinearities (RONs). For example, the problem of robust H ∞ filtering for discrete time delay with randomly occurred nonlinearities via delay-partitioning method was discussed in [27]. It should be pointed out that, up to now, the control and filtering problems for discretetime systems with RONs have not received adequate research attention yet despite their engineering importance in networked control systems.…”

H∞filtering for networked linear systems with multiple packet dropouts and random delays

“…So the obtained result is conservative. In [30], the H filtering problem is investigated by the delay partitioning method for the NCSs with the time-varying and bounded delay. But the lower bound of delay cannot be zero and the Lyapunov-Krasovskii functional candidate is complex.…”