Paper Info
Title
Control Synthesis of Hidden Semi-Markov Uncertain Fuzzy Systems via Observations of Hidden Modes.
Abstract
This paper investigates the stability analysis and fuzzy control problems for a class of discrete-time fuzzy systems with hidden semi-Markov stochastic uncertainties. The nonlinear plant is described via the Takagi–Sugeno (T–S) fuzzy model, and the parameter uncertainties are represented by a hidden semi-Markov chain. Owing to the semi-Markov kernel (SMK), the probability density functions (PDFs) of sojourn time for different modes in describing the stochastic uncertainties can address different types of distributions according to different target modes. A novel Lyapunov function that depends on the hidden mode and the observed mode with the elapsed time is proposed to analyze the stability and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> performance of the fuzzy system. Then, the sufficient criteria for the elapsed-time-dependent and observed-mode-dependent fuzzy controller are achieved by exploiting the observations of hidden modes, ensuring that the closed-loop system is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma $ </tex-math></inline-formula> -error mean square stable with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> performance. A cart–pendulum system is used to demonstrate the effectiveness and applicability of the proposed theoretical results.
Year
DOI
Venue
2020
10.1109/TCYB.2019.2921811
IEEE Transactions on Cybernetics
Keywords
DocType
Volume
Uncertainty,Markov processes,Fuzzy systems,Switches,Probability density function,Stability analysis
Journal
50
Issue
ISSN
Citations 
8
2168-2267
4
PageRank 
References 
Authors
0.39
14
3
Name
Order
Citations
PageRank
Bo Cai1263.46
Lixian Zhang23028125.86
Yang Shi3308.73