Discrete-time Markovian Systems Research Articles

A Markovian system approach to distributed H∞ filtering for sensor networks with stochastic sampling

This paper is concerned with the distributed H∞ filtering problem for a class of sensor networks with stochastic sampling. System measurements are collected through a sensor network stochastically and the phenomena such as random measurement missing and quantization are also considered. Firstly, the stochastic sampling process of the sensor network is modeled as a discrete-time Markovian system. Then, the logarithmic quantization effect is transformed into the parameter uncertainty of the filtering system, and a set of binary variables is introduced to model the random measurement missing phenomenon. Finally, the resulting augmented system is modeled as an uncertain Markovian system with multiple random variables. Based on the Lyapunov stability theory and the stochastic system analysis method, a sufficient condition is obtained such that the augmented system is stochastically stable and achieves an average H∞ performance level γ; the design procedure of the optimal distributed filter is also provided. A numerical example is given to demonstrate the effectiveness of the proposed results.

Output feedback guaranteed cost control of networked linear systems with random packet losses

This article is concerned with the output feedback guaranteed cost control problem for a class of networked control systems (NCSs) with both packet losses and network-induced delays. The packet-loss processes in the forward channel and the backward channel are modelled as two Markov chains. The dynamic output feedback controllers are considered, and the closed-loop NCS is modelled as a discrete-time Markovian system with two modes and unit time delay. By using a properly constructed Lyapunov function and the state transformation technique, a sufficient condition is derived for the closed-loop NCS to be mean-square exponentially stable and ensure a decay rate that can be tuned according to the packet loss situations in the networks. Moreover, design procedures for the guaranteed cost controllers are also presented based on the obtained stability condition and guaranteed cost performance result. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed results.

H∞ filtering of networked discrete-time systems with random packet losses

This paper studies the H ∞ filtering problem for networked discrete-time systems with random packet losses. The general multiple-input–multiple-output (MIMO) filtering system is considered. The multiple measurements are transmitted to the remote filter via distinct communication channels, and each measurement loss process is described by a two-state Markov chain. Both the mode-independent and the mode-dependent filters are considered, and the resulting filtering error system is modelled as a discrete-time Markovian system with multiple modes. A necessary and sufficient condition is derived for the filtering error system to be mean-square exponentially stable and achieve a prescribed H ∞ noise attenuation performance. The obtained condition implicitly establishes a relation between the packet loss probability and two parameters, namely, the exponential decay rate of the filtering error system and the H ∞ noise attenuation level. A convex optimization problem is formulated to design the desired filters with minimized H ∞ noise attenuation level bound. Finally, an illustrative example is given to show the effectiveness of the proposed results.