Stability Analysis of Networked Control Systems with Random Time Delays and Packet Dropouts Modeled by Markov Chains

Abstract

This paper investigates the stability analysis problem for a class of discrete-time networked control systems (NCSs) with random time delays and packet dropouts based on unified Markov jump model. The random time delays and packet dropouts existed in feedback communication link are modeled by two independent Markov chains; the resulting closed-loop system is described by a new Markovian jump linear system (MJLS) with Markov delays. Sufficient conditions of the stochastic stability for NCSs is obtained by constructing a novel Lyapunov functional, and the mode-dependent output feedback controller design method is presented based on linear matrix inequality (LMI) technique. A numerical example is given to illustrate the effectiveness of the proposed method.

Design for Nonlinear Networked Control Systems with Time Delay Governed by Markov Chain with Partly Unknown Transition Probabilities

“…according to Lemma 3, there exists matrix ∈ × such that ( ) ( ) = ( ) ; setting ( ) = ( ) , we can obtain (13) from (26). Since ( ) ( ) = ( ) , we can get…”

“…In [22,23], the random delays are modeled as Markov chains such that the closed-loop system is a jump linear system. In [24][25][26], the random time delays are modeled as Markov chains, and output feedback controller design methods for NCSs with random network-induced delays are proposed. In [27], the mixed 2 / ∞ control issue of NCSs with random time delays has been investigated based on Markov jump linear systems method.…”

“…In [27], the mixed 2 / ∞ control issue of NCSs with random time delays has been investigated based on Markov jump linear systems method. In the above literature [22][23][24][25][26][27], all parts of the elements in the transition probabilities matrix of the time delays are assumed to be completely known. However, in almost all kinds of networks, all parts of the elements in the desired transition probabilities matrix are hard or costly to obtain.…”

“…In [28][29][30], the stability issue of discrete-time networked control systems with random Markov delays and uncertain transition probabilities is studied. And the controlled plants in [22][23][24][25][26][27][28][29][30] are assumed to be linear. However, almost all the practical controlled plants are nonlinear; it is significant and necessary to further study nonlinear NCSs with partly unknown transition probabilities.…”

Observer-Based Controller Design for a Class of Nonlinear Networked Control Systems with Random Time-Delays Modeled by Markov Chains

“…Consider the classical angular positioning system shown in Figure 4, which consists of a rotating antenna at the origin of the plane driven by a motor [23].…”