Stabilization for Networked Control System With Time-Delay and Packet Loss in Both S-C Side and C-A Side

Abstract

The stabilization problem for a class of discrete network control system with time-delay and packet loss in both S-C side and C-A side is researched in this paper. Firstly, two independent discrete Markov chains are used to describe the network time-delay from sensor to controller and the network time-delay from controller to actuator. Two random variables obeying the Bernoulli distribution are employed to describe the packet loss between the sensor and the controller and the packet loss between the controller and the actuator. Secondly, a mathematical model for closed-loop system is established. By constructing the appropriate Lyapunov-Krasovskii functional, the sufficient conditions for the existence of the controller and observer gain matrix are obtained under the condition that the transition probabilities of S-C time-delay and C-A time-delay are both partly unknown. Finally, two examples are exploited to illustrate the effectiveness of the proposed method.

H ∞ Control of Networked Control System With Data Packet Dropout via Observer-Based Controller

“…Since (17) holds for any ζ k , one has P r k = lim T →∞P r k . Because Z r t > 0, it can be obtained that P r k > 0 from (17). Moreover, one has:…”

“…Letting Y p = P −1 p , p ∈ M, and by applying the Schur complement, r k < 0 is equivalent to (17). Hence, it can be concluded from (17) and (19) that…”

“…The conditions presented in Theorem 2 are a set of LMIs with some matrices inverse constraints which can be solved by the cone complementary linearization (CCL) algorithm. The problem of solving the controller gain matrix K and the observer gain matrix L can be transformed into the following nonlinear minimization problem: (17) and (21).…”

“…The second type of method is to model the phenomenon of data packet dropout as a binary switching sequence taking values of zero or one which is specified by a Bernoulli probability distribution (see, e.g., [13]- [17]). For a class of NCS with random data packet dropout, a novel robust model predictive control method with active compensation mechanism was proposed.…”

“…The data packet dropout in S-C link and C-A link was described by two random variables obeying the Bernoulli distribution, respectively. The sufficient conditions on the existence of the controller were established by constructing the appropriate Lyapunov-Krasovskii functional [17].…”