A delay-dependent approach toH_∞filtering for stochastic delayed jumping systems with sensor non-linearities

Abstract

In this paper, a delay-dependent approach is developed to deal with the stochastic H ∞ filtering problem for a class of Itô type stochastic time-delay jumping systems subject to both the sensor nonlinearities and the exogenous nonlinear disturbances. The time delays enter into the system states, the sensor nonlinearities and the external nonlinear disturbances. The purpose of the addressed filtering problem is to seek an H ∞ filter such that, in the simultaneous presence of nonlinear disturbances, sensor nonlinearity as well as Markovian jumping parameters, the filtering error dynamics for the stochastic time-delay system is stochastically stable with a guaranteed disturbance rejection attenuation level γ. By using Itô's differential formula and the Lyapunov stability theory, we develop a linear matrix inequality approach to derive sufficient conditions under which the desired filters exist. These conditions are dependent on the length of the time delay. We then characterize the expression of the filter parameters, and use a simulation example to demonstrate the effectiveness of the proposed results. SUBMITTED 2 Consequently, the time delay systems with stochastic perturbations have drawn a lot of attentions from researchers working in related areas, see [1,21,22] and references therein.Markovian jump systems are the hybrid systems with two components in the state [11]. The first one refers to the mode which is described by a continuous-time finite-state Markovian process, and the second one refers to the state which is represented by a system of differential equations. The jump systems have the advantage of modeling the dynamic systems subject to abrupt variation in their structures, such as component failures or repairs, sudden environmental disturbance, changing subsystem interconnections, operating in different point of a nonlinear plant. Recently, filtering and control for Markovian jump systems with or without nonlinear disturbances have drawn some research attentions, see [17,23,24,27,28] for some related results. Note that exogenous nonlinear disturbances may result from the linearization process of an originally highly nonlinear plant or may be an external nonlinear input, and therefore exist in many real-world systems.The filter design problem has long been one of the key problems in the areas of control and signal processing. The purpose of the filtering problem is to estimate the unavailable state variables (or a linear combination of the states) of a given system through noisy measurements. During the past four decades, the filtering problem has been extensively investigated for a variety of complex systems, such as deterministic delay systems [1,8,9], Markovian jumping delay systems [17,20,23] and stochastic delay systems [22,24], to name just a few. When both the Markovian jump parameters and time delays appear in the stochastic systems, the H ∞ filtering problem has been studied in [24], where some useful stochastic stability conditions have been proposed by an LMI technique. In [23], the robust H...

Exponential H_infinity filter design for stochastic Markovian jump systems with both discrete and distributed time-varying delays

“…To the best of the authors' knowledge, the decay rate β in many literatures is a fixed value computed by solving a transcendental equation or inequality, for example [1,24,29,38,44]. Moreover, these results can not tell us whether a system can possess a larger decay rate than the computed value.…”

“…In [23], the DOI: 10.14736/kyb-2014- author explains that jump systems have been emerging as an effective framework for various control problems in different fields such as target tracking, manufacturing processes, and fault-tolerant control systems. Many interesting results on stochastic systems with time delays have been presented, e. g., [2,5,14,15,21,22,24,28,29,38,39,40,41,42,43] and references therein.…”

Robust $H_{\infty}$ Filtering for a Class of Nonlinear Networked Systems With Multiple Stochastic Communication Delays and Packet Dropouts

“…These specialized results are not listed here to keep the exposition concise. It is also worth pointing out that the main results in this paper can be easily extended to the delayed jumping systems with sensor nonlinearities [24] and other more complicated systems. Note that we mainly focus on the effects brought by multiple stochastic communication delays and packet dropouts, which are two of the most important network-induced characteristics.…”

“…Furthermore, recognizing that both nonlinearity and stochasticity are commonly encountered in engineering practice, the robust filtering problems for nonlinear stochastic systems have stirred a great deal of research interests. For example, the stochastic filtering problem for time-delay systems subject to sensor nonlinearities have been dealt with in [23] and [24]. In [32], the robust filtering problem for affine nonlinear stochastic systems with state and external disturbance-dependent noise has been studied, where the filter can be designed by solving second-order nonlinear Hamilton-Jacobi inequalities.…”

$$H_\infty $$ H ∞ filtering for stochastic singular fuzzy systems with time-varying delay

“…It should be noted that the H ∞ filtering problem of linear systems has been studied, and a great number of results have been reported (see [20][21][22]). However, compared with linear systems, the H ∞ filtering problem for nonlinear systems has not been fully investigated although it is important in control design and signal processing [23,24].…”