Piecewise quadratic stability of fuzzy systems

Johansson, Mikael; Rantzer, Anders; Årzén, Karl-Erik

doi:10.1109/91.811241

Cited by 704 publications

(324 citation statements)

References 15 publications

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“…By 2005, there existed a large body of literature on stability analysis and design of T-S fuzzy control systems. Improvements have appeared in piecewise/gridpoint approaches [37,38], non-PDC design [39,40,41], multi-step non-monotonic Lyapunov functions [42], and LinearFractional transformation approaches to fuzzy modelling [27], with clear links to the LPV gain-scheduling concepts [18]. Widely used relaxations of the double-summation problem (which apply to many fuzzy results) appeared in [43,44], although conservatism remained.…”

Section: Model-based Fuzzy Control Designmentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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In 2015, we celebrate the 50th anniversary of Fuzzy Sets, ten years after the main milestones regarding its applications in fuzzy control in their 40th birthday were reviewed in FSS, see [1]. Ten years is at the same time a long period and short time thinking to the inner dynamics of research. This paper, presented for these 50 years of Fuzzy Sets is taking into account both thoughts. A first part presents a quick recap of the history of fuzzy control: from model-free design, based on human reasoning to quasi-LPV (Linear Parameter Varying) model-based control design via some milestones, and key applications. The second part shows where we arrived and what the improvements are since the milestone of the first 40 years. A last part is devoted to discussion and possible future research topics.

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Section: Model-based Fuzzy Control Designmentioning

confidence: 99%

Fuzzy control turns 50: 10 years later

Guerra

Sala

Tanaka

2015

Fuzzy Sets and Systems

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“…The design problem on non-uniform discrete-time domains can be successfully approached by exploiting interesting results on robust stability (see [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]) for perturbed systems of type…”

Section: Robust Stability Of Time-varying Linear Systemsmentioning

confidence: 99%

“…Further robust stability conditions have been obtained using LMI techniques (see [20,22,23,25]) and H 1 and H ∞ formulations (see [19,21,24]). Such approaches will be evaluated in future work.…”

Section: Is the Solution Of The Discrete-time Lyapunov Equationmentioning

confidence: 99%

Controller Synthesis on Non-uniform and Uncertain Discrete–Time Domains

Balluchi¹,

Murrieri²,

Sangiovanni‐Vincentelli

2005

Hybrid Systems: Computation and Control

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Abstract. The problem of synthesizing feedback controllers that perform sensing and actuation actions on non-uniform and uncertain discrete time domains is considered. This class of problems is relevant to many application domains. For instance, in engine control a heterogenous and, to some extent, uncertain event-driven time domain is due to the behavior of the 4-stroke internal combustion engine, with which the controller has to synchronize to operate properly. Similar problems arise also in standard discrete-time control systems when considering the behavior of the system with controller implementation and communication effects. The design problem is formalized in a hybrid system framework; synthesis and verification methods, based on robust stability and robust performance results, are presented. The effectiveness of the proposed methods is demonstrated in an engine control application.

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“…One of the successful approaches to less conservative stability analysis and stabilization design is based on the so-called piecewise quadratic Lyapunov functions [1,10,11,15]. Another approach to reducing the conservatism in stability analysis or stabilization results is to adopt fuzzy Lyapunov functions [27].…”

Section: Introductionmentioning

confidence: 99%