Markov Jump Linear Systems with switching transition rates: Mean square stability with dwell-time

Automatica ◽  
2010 ◽  
Vol 46 (6) ◽  
pp. 1081-1088 ◽  
Author(s):  
Paolo Bolzern ◽  
Patrizio Colaneri ◽  
Giuseppe De Nicolao
Keyword(s):  
Linear Systems ◽  
Dwell Time ◽  
Transition Rates ◽  
Mean Square ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Mean Square Stability ◽  
Markov Jump Linear Systems

Receding Horizon Control for Uncertain Markov Jump Linear Systems with Time Delay and Actuator Saturation

2013 ◽  
Vol 303-306 ◽  
pp. 1193-1199 ◽  
Author(s):  
Ji Wei Wen
Keyword(s):  
Time Delay ◽  
Linear Systems ◽  
Actuator Saturation ◽  
Receding Horizon Control ◽  
Receding Horizon ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Current Time ◽  
Mean Square Stability ◽  
Markov Jump Linear Systems

A robust receding horizon control (RHC) scheme is developed for uncertain discrete-time Markov Jump Linear Systems (MJLS) with time delay and actuator saturation where the system uncertainties and jumping transition probabilities are assumed to belong to some convex sets. Firstly, when time delay is considered, a sufficient condition of minimizing upper bound of the cost function and mean square stability of the closed-loop system are established based on the Lyapunov Krasovskii function which depend on the current time jump mode. At each sampling time, an optimal control gain can be obtained by solving the semi-definite programming (SDP) problem. Then, the proposed strategy is extended to design robust RHC scheme for uncertain MJLS with both time delay and actuator saturation. Moreover, the domain of attraction can be estimated through a modified invariant ellipsoid. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the proposed method.

Stability Analysis for Discrete-Time Markov Jump System

2012 ◽  
Vol 249-250 ◽  
pp. 1224-1227
Author(s):  
Ming Wei Li ◽  
Yi Chen ◽  
Xiao Han Zhang
Keyword(s):  
Linear Systems ◽  
Data Packet ◽  
Linear Matrix ◽  
Packet Dropout ◽  
Mean Square ◽  
Markov Jump ◽  
Jump Linear Systems ◽  
Data Packet Dropout ◽  
Markov Jump System ◽  
Markov Jump Linear Systems

Network control systems (NCSs) where the problems of data packet dropout induced by communication channel is studied in this paper. We model the data packet dropout a Markov Jump Linear systems and introduce a freedom matrix. Our goal is to find a controller such that the Markov Jump Linear systems mean square stable. According to linear matrix inequalities (LMI), we can get the sufficient condition on the mean square stabilization of NCSs. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed approach.

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