Parameterized linear matrix inequality techniques in fuzzy control system design

By Hoang Duong Tuan, Pierre Apkarian, T. Narikiyo, Y. Yamamoto. IEEE transactions on fuzzy systems, 2001

1,200 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/5b6af3dfa7a3bcaae68ee06d4df6263239ed4ee3

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Jianbin Qiu
2. Gang Feng
3. Jie Yang
4. Peng Shi
5. Ligang Wu
6. Xiaojie Su
7. Bin Jiang
8. Sangchul Won

In Computational Theory and Mathematics

1. Peng Shi
2. Gang Feng
3. Bin Jiang
4. Sangchul Won
5. Robert Babuška
6. Huai‐Ning Wu
7. Ligang Wu
8. Jianbin Qiu

In Control and Systems Engineering

1. Jianbin Qiu
2. Peng Shi
3. Ligang Wu
4. Gang Feng
5. Yongduan Song
6. Xiaojie Su
7. Jie Yang
8. Antonio Sala

Citations in the corpus

• Mode-independent robust stabilization for uncertain Markovian jump nonlinear systems via fuzzy control (2005, background): “2 in [8] to the inequalities of (34), it is easily obtained that if there exist a common matrix P = P T > 0 and matrices Y j , j ∈ S satisfying the following LMIs Ψk,ii < 0, i ∈ S, k ∈ T (43) 1 r − 1k,ii + 1 2 (Ψk,ij +Ψk,ji) < 0, i = j∈S, k∈T (44)”
• A Survey on Analysis and Design of Model-Based Fuzzy Control Systems (2006, background): “8), or to reduce its conservatism, or both [142], [192], [198], [267], [275], [286], [304].”
• A Novel Control Design on Discrete-Time Takagi–Sugeno Fuzzy Systems With Time-Varying Delays (2013, methodology): “Based on the fuzzy basis functions and [24], from (20)–(23) we obtain ∑r”
• A new fuzzy Lyapunov function approach for a Takagi-Sugeno fuzzy control system design (2006, methodology): “For the better relaxation, the other method in [8,17,19] can be applied as mentioned in Remark 4.”
• Adaptive Fault-Tolerant Tracking Control of Near-Space Vehicle Using Takagi–Sugeno Fuzzy Models (2010, background): “[25], is satisfied if the conditions (14) and (15) hold.”
• A New Design of Delay-Dependent Robust ${\cal H}_{\bm \infty}$ Filtering for Discrete-Time T--S Fuzzy Systems With Time-Varying Delay (2009, methodology): “4: It is noted that the convexifying procedure proposed in this paper is based on the relaxation inequality (51), and extensions of the current derivations based on the more powerful relaxation techniques presented in [7] and [16]–[22] are straightforward.”
• Perspectives of fuzzy systems and control (2005, background): “Another approach is to use some matrix properties: specific transformations, elimination lemma [59] and/or relaxation of the basic inequality (6), see for example [52,35].”
• An alternative to inverse dynamics joint torques estimation in human stance based on a Takagi–Sugeno unknown-inputs observer in the descriptor form (2008, methodology): “■ Note that it is straightforward to apply any relaxation schemes found in the literature in addition to the conditions given in theorem 1 (Liu and Zhang, 2003; Tuan et al., 2001).”
• Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach (2008, background): “Several ways are possible: matrix properties with specific transformations [12], [13], elimination lemma [14], relaxation of the basic inequalities [5], [6].”
• A New Approach to Stability Analysis and Stabilization of Discrete-Time T-S Fuzzy Time-Varying Delay Systems (2011, background): “Some of the existing results were usually derived by using a single Lyapunov function method [21], [24], the main drawback of which is that it leads to conservative results.”