Title :
Stability and stabilization for nonlinear discrete-time singular Markov jump systems with time-varying delay
Author :
Rui Wang ; Shuping Ma
Author_Institution :
Sch. of Math., Shandong Univ., Jinan, China
Abstract :
In this paper, stability and state feedback stabilization for nonlinear discrete-time singular Markov jump systems with time-varying delay is discussed. Based on Lyapunov theory and the implicit function theorem, a linear matrix inequality (LMI) sufficient condition is developed which guarantees that the nonlinear discrete-time singular Markov jump systems with time-varying delay are regular, causal, have unique solution in a neighborhood of the equilibrium point, and are stochastically stable. Then, in order to facilitate the design of the controller, based on this stability condition, by using a series of matrix inequalities, another LMI stability condition is obtained, and the design method of state feedback controllers is given. Last, a numerical example is given to show the effectiveness and correctness of the proposed method.
Keywords :
Lyapunov methods; control system synthesis; delays; discrete time systems; linear matrix inequalities; nonlinear control systems; stability; state feedback; stochastic systems; time-varying systems; LMI stability condition; LMI sufficient condition; Lyapunov theory; equilibrium point; implicit function theorem; linear matrix inequality sufficient condition; nonlinear discrete-time singular Markov jump system stabilization; regular-causal systems; state feedback controller design method; state feedback stabilization; stochastically stable system; time-varying delay; Delays; Electronic mail; Markov processes; Nickel; Numerical stability; State feedback; Time-varying systems; Discrete-time singular Markov jump system; Nonlinear; Stability; State feedback stabilization; Time-varying delay;
Conference_Titel :
Control and Decision Conference (CCDC), 2013 25th Chinese
Conference_Location :
Guiyang
Print_ISBN :
978-1-4673-5533-9
DOI :
10.1109/CCDC.2013.6561625