Fuzzy control and filter design for uncertain fuzzy systems

Most real physical systems are nonlinear in nature. Control and ?ltering of nonlinear systems are still open problems due to their complexity natures. These problem becomes more complex when the system's parameters are - certain. A common approach to designing a controller/?lter for an uncertain nonlinear system is to linearize the system about an operating point, and uses linear control theory to design a controller/?lter. This approach is successful when the operating point of the system is restricted to a certain region. H- ever, when a wide range operation of the system is required, this method may fail. ThisbookpresentsnewnovelmethodologiesfordesigningrobustH fuzzy ? controllers and robustH fuzzy ?lters for a class of uncertain fuzzy systems ? (UFSs), uncertain fuzzy Markovian jump systems (UFMJSs), uncertain fuzzy singularly perturbed systems (UFSPSs) and uncertain fuzzy singularly p- turbed systems with Markovian jumps (UFSPS-MJs). These new meth- ologies provide a framework for designing robustH fuzzy controllers and ? robustH fuzzy ?lters for these classes of systems based on a Tagaki-Sugeno ? (TS) fuzzy model. Solutions to the design problems are presented in terms of linear matrix inequalities (LMIs). To investigate the design problems, we ?rst describe a class of uncertain nonlinear systems (UNSs), uncertain nonlinear Markovianjumpsystems(UNMJSs),uncertainnonlinearsingularlyperturbed systems(UNSPSs)anduncertainnonlinearsingularlyperturbedsystemswith Markovian jumps (UNSPS-MJs) by a TS fuzzy system with parametric - certainties and with/without Markovian jumps. Then, based on an LMI - proach, we develop a technique for designing robustH fuzzy controllers and ? robustH fuzzy ?lters such that a given prescribed performance index is ? guaranteed.

1 Introduction	p. 1
1.1 Preliminary Background	p. 1
1.2 Motivation	p. 3
1.3 Contribution of the Book	p. 4
1.4 Book Organization	p. 5
Part I Uncertain Fuzzy Systems
2 Uncertain Fuzzy Systems	p. 9
2.1 Background and Motivation	p. 9
2.1.1 TS Fuzzy Modelling	p. 10
2.1.2 TS fuzzy Controller	p. 14
2.2 Outline of Part I	p. 16
3 Robust H[subscript Infin] Fuzzy Control Design for Uncertain Fuzzy Systems	p. 17
3.1 System Description	p. 17
3.2 Robust H[subscript Infin] State-Feedback Control Design	p. 18
3.3 Robust H[subscript Infin] Output Feedback Control Design	p. 19
3.3.1 Case I-v(t) is available for feedback	p. 20
3.3.2 Case II-v(t) is unavailable for feedback	p. 23
3.4 Example	p. 26
3.5 Conclusion	p. 31
4 Robust H[subscript Infin] Fuzzy Filter Design for Uncertain Fuzzy Systems	p. 33
4.1 Robust H[subscript Infin] Fuzzy Filter Design	p. 33
4.1.1 Case I-v(t) is available for feedback	p. 34
4.1.2 Case II-v(t) is unavailable for feedback	p. 38
4.2 Example	p. 40
4.3 Conclusion	p. 45
5 Robust H[subscript Infin] Fuzzy Control Design for Uncertain Fuzzy Markovian Jump Systems	p. 47
5.1 System Description	p. 47
5.2 Robust H[subscript Infin] State-Feedback Control Design	p. 49
5.3 Robust H[subscript Infin] Output Feedback Control Design	p. 50
5.3.1 Case I-v(t) is available for feedback	p. 50
5.3.2 Case II-v(t) is unavailable for feedback	p. 54
5.4 Example	p. 57
5.5 Conclusion	p. 64
6 Robust H[subscript Infin] Fuzzy Filter Design for Uncertain Fuzzy Markovian Jump Systems	p. 65
6.1 Robust H[subscript Infin] Fuzzy Filter Design	p. 65
6.1.1 Case I-v(t) is available for feedback	p. 66
6.1.2 Case II-v(t) is unavailable for feedback	p. 69
6.2 Example	p. 71
6.3 Conclusion	p. 78
Part II Uncertain Fuzzy Singularly Perturbed Systems
7 Uncertain Fuzzy Singularly Perturbed Systems	p. 81
7.1 Background and Motivation	p. 81
7.2 Outline of Part II	p. 83
8 Robust H[subscript Infin] Fuzzy Control Design for Uncertain Fuzzy Singularly Perturbed Systems	p. 85
8.1 System Description	p. 85
8.2 Robust H[subscript Infin] State-Feedback Control Design	p. 86
8.3 Robust H[subscript Infin] Output Feedback Control Design	p. 89
8.3.1 Case I-v(t) is available for feedback	p. 89
8.3.2 Case II-v(t) is unavailable for feedback	p. 92
8.4 Example	p. 94
8.5 Conclusion	p. 99
9 Robust H[subscript Infin] Fuzzy Filter Design for Uncertain Fuzzy Singularly Perturbed Systems	p. 101
9.1 Robust H[subscript Infin] Fuzzy Filter Design	p. 101
9.1.1 Case I-v(t) is available for feedback	p. 102
9.1.2 Case II-v(t) is unavailable for feedback	p. 104
9.2 Example	p. 106
9.3 Conclusion	p. 111
10 Robust H[subscript Infin] Fuzzy Control Design for Uncertain Fuzzy Singularly Perturbed Systems with Markovian Jumps	p. 113
10.1 System Description	p. 113
10.2 Robust H[subscript Infin] State-Feedback Control Design	p. 114
10.3 Robust H[subscript Infin] Fuzzy Output Feedback Control Design	p. 118
10.3.1 Case I-v(t) is available for feedback	p. 118
10.3.2 Case I-v(t) is unavailable for feedback	p. 122
10.4 Example	p. 125
10.5 Conclusion	p. 133
11 Robust H[subscript Infin] Fuzzy Filter Design for Uncertain Fuzzy Singularly Perturbed Systems with Markovian Jumps	p. 135
11.1 Robust H[subscript Infin] Fuzzy Filter Design	p. 135
11.1.1 Case I-v(t) is available for feedback	p. 136
11.1.2 Case II-v(t) is unavailable for feedback	p. 139
11.2 Example	p. 141
11.3 Conclusion	p. 148
A Proof	p. 149
References	p. 169

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