Observer‐based H_∞ control of discrete Markovian jump delay systems with random packet losses and multiplicative noises

Abstract

SUMMARYThis paper investigates the observer‐based H ∞ control problem for a class of mixed‐delay Markovian jump systems with random communication packet losses and multiplicative noises. The mixed delays comprise both discrete time‐varying delays and distributed delays, the random packet losses are described by a Bernoulli distributed white sequence that obeys a conditional probability distribution, and the multiplicative disturbances are in the form of a scalar Gaussian white noise with unit variance. In the presence of mixed delays, random packet losses and multiplicative noises, sufficient conditions for the existence of an observer‐based feedback controller are derived such that the closed‐loop control system is asymptotically mean‐square stable and preserves a guaranteed H ∞ performance. Then, a linear matrix inequality approach for designing such an observer‐based H ∞ controller is presented. Finally, a numerical example is provided to illustrate the effectiveness of the developed theoretical results. Copyright © 2012 John Wiley & Sons, Ltd.

Finite-timeH∞control for stochastic time-delayed Markovian switching systems with partly known transition rates and nonlinearity

“…Recently, extensive studies on Markovian switching system with time delay have been done, including stability analysis (He & Liu, 2011;Wu, Park, Su, & Chu, 2012), stabilisation (Fei, Gao, & Shi, 2009), output feedback design (Dong & Kim 2012), H ∞ control (Cheng, Zhu, Zhong, Zeng, & Dong, 2013), filter design (Wang, 2011;Yan, Meng, Zhang, & Shi, 2010) and observer design (Gao, Wang, & Wu, 2014;Wen, Zeng, Huang, & Bao, 2013).…”

Observer‐based dissipative control for networked control systems: A switched system approach

“…Hence, the observer-based dissipative controller for wireless NCS (1) can be designed in terms of the feasible solutions to a set of LMIs (13)- (15). It should be noted that here the LMI (15) can be used instead of SVD, so it is necessary that the matrix F 2 R n3n .…”

“…So, the issues like packet dropouts and network-induced delay have been widely studied by many researchers, see [10][11][12][13][14]. Wen et al, [15] studied the observer-based H 1 control problem for a class of mixed-delay Markovian jump systems with random communication packet losses and multiplicative noises. Stability analysis and state feedback controller design of NCSs with multiple-packet transmission and packet dropout in both the sensor-to-controller and controller-to-actuator is given in [16].However, in practice, the state variables are often unknown or partially known, in other words, not always measurable.…”