Robust reliable control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises

Abstract

This paper is concerned with the reliable control problem against actuator failures for a class of uncertain discrete-time stochastic nonlinear time-delay systems. The failures of actuators are quantified by a variable varying in a given interval. The stochastic nonlinearities described by statistical means cover several well-studied nonlinear functions as special cases. The time-varying delay is unknown with given lower and upper bounds. The multiplicative stochastic disturbances are in the form of a scalar Gaussian white noise with unit variance. Attention is focused on the analysis and design of a stable controller such that, for all possible actuator failures, stochastic nonlinearities and disturbances, time delays and admissible parameter uncertainties, the closed-loop system is exponentially mean-square stable. A linear matrix inequality approach is developed to solve the addressed problem. A numerical example is given to demonstrate the effectiveness of the proposed design approach. of well-studied nonlinear systems, for example, the nonlinear systems with random sequences whose powers depend on the sector-bound nonlinear function of the state.Recently, stochastic systems with multiplicative noises (also called bilinear systems or systems with state-dependent noises) have received much attention since many plants may be modelled by systems with multiplicative noises, and some characteristics of nonlinear systems can be closely approximated by models with multiplicative noises rather than by linearized models [9]. In [2], both the control and filtering problems have been investigated for discrete-time stochastic systems with multiplicative noise. Furthermore, in [3], the robust variance-constrained H ∞ control problem has been studied for stochastic systems with multiplicative noises, where two additional optimization problems have been formulated: one is to optimize the H ∞ performance and the other is to minimize the weighted sum of the system state variances.On the other hand, it is inevitable that there exist time delays in dynamic systems due to measurement, transmission and transport lags, computational delays, or unmodelled inertia of system components, which has been known as a main source to degrade the performance of the control system. Therefore, the study for time-delay systems has attracted considerable research interests and various approaches have been proposed in the literature. Generally, the existing approaches can be classified into two categories: delay-independent approach that is applicable to delays of arbitrary length [10-14] and delay-dependent approach that makes use of information on the length of delays [15][16][17][18][19][20]. Since the stability of systems explicitly depends on the time-delay, the delay-dependent approach is generally regarded as being less conservative than the delayindependent one, especially in situations where delays are small. Therefore, the delay-dependent approach has been extensively exploited in recent research for time-delay systems.In practical appl...

Reliable H∞ Filtering for Mixed Time‐Delay Systems with Stochastic Nonlinearities and Multiplicative Noises

“…(iii) The stochastic nonlinearities and multiplicative noises have been considered in the design of reliable H ∞ filter. (iv) An LMI approach is developed to solve the reliable H ∞ filtering problem, where both mean‐square stability and H ∞ constraints are guaranteed simultaneously. Remark Based on , this paper investigates the H ∞ filtering problem for the systems with mixed time delays, stochastic nonlinearities, multiplicative noises, and sensor failures; therefore, the results obtained can be used more widely than several existing results. (i) When the distributed delays and multiplicative noises are not taken into account, the obtained results can be used to solve the filtering problem about discrete‐time‐delay systems in .…”

“…(i) When the distributed delays and multiplicative noises are not taken into account, the obtained results can be used to solve the filtering problem about discrete‐time‐delay systems in . (ii) When the distributed delays are not considered, the theoretical results in this paper can be used to solve the reliable H ∞ control for discrete‐time‐delay systems with stochastic nonlinearities and multiplicative noises in . (iii) When the sensor failures and multiplicative noises are not taken into consideration, the obtained results in this paper can be used to design the controller for discrete‐time stochastic systems with distributed delays and nonlinear disturbances in .…”

Recent Progress in Stability and Stabilization of Systems with Time-Delays

“…(vii) The class of uncertain nonlinear networked systems with both multiple stochastic time-varying communication delays and multiple packet dropouts was addressed in [84] for filtering design and in [85] for reliable control. A promising research direction is to extend the role of delay patterns to alternative forms.…”

Robust reliable control design for networked control system with sampling communication

“…In literature there have been many approaches proposed to design the reliable controllers, see Gao et al (2013); Gu et al (2012); Mahmoud (2012). Liu et al (2011) proposed a reliable control design against actuator failures for a class of discrete-time stochastic nonlinear time-delay systems.…”