Mean square stability for Kalman filtering with Markovian packet losses

This paper addresses the mean square stabilization problem for discrete-time networked control systems over fading channels. We show that there exists a requirement on the network over which an unstable plant can be stabilized. In the case of state feedback, necessary and sufficient conditions on the network for mean square stabilizability are derived. Under a parallel transmission strategy and the assumption that the overall mean square capacity of the network is fixed and can be assigned among parallel input channels, a tight lower bound on the overall mean square capacity for mean square stabilizability is presented in terms of the Mahler measure of the plant. The minimal overall capacity for stabilizability is also provided under a serial transmission strategy. For the case of dynamic output feedback, a tight lower bound on the capacity requirement for stabilization of SISO plants is given in terms of the anti-stable poles, nonminimum phase zeros and relative degree of the plant. Sufficient and necessary conditions are further derived for triangularly decoupled MIMO plants. The effect of pre- and post-channel processing and channel feedback is also discussed, where the channel feedback is identified as a key component in eliminating the limitation on stabilization induced by the nonminimum phase zeros and high relative degree of the plant. Finally, the extension to the case with output fading channels and the application of the results to vehicle platooning are presented.

Feedback Stabilization of Discrete-Time Networked Systems Over Fading Channels

In this paper, we study the $H_{2} $ -control for discrete-time Markov Jump Linear Systems (MJLS) with partial information . We consider the case in which we do not have access to the Markov jump parameter but, instead, there is a detector that emits signals which provides information on this parameter. A salient feature of our formulation is that it encompasses, for instance, the cases with perfect information, no information and cluster observations of the Markov parameter, which were previously analyzed in the Markov jump control literature. The goal is to derive a feedback linear control using the information provided by the detector in order to stochastically stabilize the closed loop system. We present two Lyapunov like equations for the stochastic stability of the system. In addition, we show that a Linear Matrix Inequalities (LMI) formulation can be obtained in order to design a stochastically stabilizing feedback control. In the sequel we deal with the $H_{2} $ control problem and we show that, again, an LMI optimization problem can be formulated in order to design a stochastically stabilizing feedback control with guaranteed $H_{2} $ -cost. We also present two special cases, one of them always satisfied for the limit case in which the detector provides perfect information on the Markov parameter, and the Bernoulli jump case, under which LMI conditions become necessary and sufficient for the stochastic stabilizability of the system and the LMI optimization problems provide the optimal $H_{2} $ cost. For the Bernoulli jump case we show that our formulation generalizes previous ones. The case with convex polytopic uncertainty on the parameters of the system and on the transition probability matrix is also considered. The paper is concluded with some numerical examples.

A Detector-Based Approach for the $H_{2} $ Control of Markov Jump Linear Systems With Partial Information

https://dr.ntu.edu.sg/bitstream/10356/107210/1/Survey%20of%20Recent%20Progress%20in%20Networked%20Control%20Systems.pdf

Survey of recent progress in networked control systems

Brief paper: Stabilization of Markov jump linear systems using quantized state feedback

Brief paper: Stability robustness of networked control systems with respect to packet loss

This paper is concerned with stability analysis of discrete-time networked control systems subject to packet loss under a multiple-packet transmission policy with the packet dropping probability of the communication channel bounded from above. Necessary and sufficient conditions for stability are obtained. In addition, the packet dropping margin as a measure of stability robustness of a system against packet loss is defined and its formula is derived. A design method is proposed for enhancing stability robustness subject to the constraint of a set of prescribed nominal closed-loop poles.

Stability of Networked Control Systems Under a Multiple-Packet Transmission Policy

This paper is concerned with stability analysis of discrete-time networked control systems in the case where both input and output channels are characterized by a multiplepacket transmission policy. A necessary and sufficient condition for stability is obtained for known packet dropping probabilities. The issue of stability robustness of a system against packet dropping is discussed and addressed in the case of uncertain packet dropping probabilities.

Shawn Hu

Papers

Brief paper: Stability robustness of networked control systems with respect to packet loss

Stability of Networked Control Systems Under a Multiple-Packet Transmission Policy

Stability of networked control systems subject to input and output packet loss