scholarly journals $H_{\infty}$ Controller Design for Singular Stochastic Markovian Jump System With Time-Varying Delay

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 147883-147891 ◽  
Author(s):  
Yuanhua Du ◽  
Yuqian Zhou ◽  
Kaibo Shi ◽  
Yaoru Yang
Keyword(s):  
Controller Design ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Time Varying Delay ◽  
Varying Delay

Parallel distributed compensation controller design for Markovian jump system with time-varying delays using Bessel-Legendre inequality method and improved positive definite rule

2019 ◽  
Vol 42 (7) ◽  
pp. 1313-1322
Author(s):  
Nuo Xu ◽  
Liankun Sun
Keyword(s):  
Controller Design ◽  
Positive Definite ◽  
Practical Significance ◽  
Time Varying ◽  
Markovian Jump ◽  
Actual System ◽  
Pendulum System ◽  
Markovian Jump System ◽  
Time Varying Delay ◽  
Inverted Pendulum System

In this paper, based on time-varying delay Markovian jump system (MJS), Bessel-Legendre inequality method and improved positive definite condition of Lyapunov function are used, and parallel distributed compensation (PDC) state feedback controller is also introduced. The conservatism of the system is reduced by using this inequality method and positive definite conditions, and further decreases with the increase of the Legendre parameter N. The PDC controller considers two control parameters simultaneously, which can represent the actual system more truthfully. Finally, Example 1 proves the effectiveness of the improved method in this paper. Example 2 considers time-varying probability transition perturbations. Example 3 obtains the parameters of PDC controller with different parameters N. Example 4 illustrates the practical significance of methods in this paper by introducing a time-delay inverted pendulum system with Markovian parameters.

scholarly journals Exponential Stability in Mean Square of Singular Markovian Jump System with Saturating Actuators and Time-Varying Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Fangqing Ding ◽  
Xianfa Jiao
Keyword(s):  
Exponential Stability ◽  
Time Varying ◽  
Mean Square ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Time Varying Delay ◽  
Saturating Actuators ◽  
Singular Markovian Jump Systems ◽  
Varying Delay ◽  
Stability In Mean Square

This paper investigates exponential stability in mean square of singular Markovian jump systems with saturating actuators and time-varying delay. The statistical property of the Markov process is fully used to derive the differential of the function. By using a delay decomposition method, a mode-dependent Lyapunov-Krasovskii function is established. A sufficient condition is proposed for exponential stability in mean square of the system designing the memoryless state feedback. A numerical example shows that the approach proposed is effective.

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