scholarly journals Stability Analysis of Markovian Jump System With Multi-Time-Varying Disturbances Based on Improved Interactive Convex Inequality and Positive Definite Condition

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 54910-54917 ◽  
Author(s):  
Liankun Sun ◽  
Nuo Xu
Keyword(s):  
Stability Analysis ◽  
Positive Definite ◽  
Time Varying ◽  
Markovian Jump ◽  
Markovian Jump System ◽  
Definite Condition ◽  
Convex Inequality

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 Stability Analysis of Drilling Inclination System with Time-Varying Delay via Free-Matrix-Based Lyapunov–Krasovskii Functional

2021 ◽  
Vol 25 (6) ◽  
pp. 1031-1038
Author(s):  
Zhen Cai ◽  
Guozhen Hu ◽  
◽  
Keyword(s):  
Stability Analysis ◽  
Asymptotic Stability ◽  
Stability Criterion ◽  
Coefficient Matrix ◽  
Positive Definite ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Stability ◽  
Varying Delay ◽  
Insight Into

This study provides an insight into the asymptotic stability of a drilling inclination system with a time-varying delay. An appropriate Lyapunov–Krasovskii functional (LKF) is essential for the stability analysis of the abovementioned system. In general, an LKF is constructed with each coefficient matrix being positive definite, which results in considerable conservatism. Herein, to relax the conditions of the derived criteria, a novel LKF is proposed by avoiding the positive-definite restriction of some coefficient matrices and introducing additional free matrices simultaneously. Subsequently, this relaxed LKF is applied to derive a less conservative stability criterion for the abovementioned system. Finally, the effect of reducing the conservatism of the proposed LKF is verified based on two examples.

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