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Improved Adaptive H ∞ Controller Synthesis of Piecewise‐Affine Systems
Author(s) -
Zhang Hongwen,
Liu Kai,
Zhang Shangmin,
Qiao Hong,
Qiu Bobo
Publication year - 2017
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1523
Subject(s) - piecewise , mathematics , control theory (sociology) , lyapunov function , projection (relational algebra) , controller (irrigation) , quadratic equation , lemma (botany) , mathematical optimization , computer science , control (management) , nonlinear system , algorithm , mathematical analysis , ecology , physics , geometry , poaceae , quantum mechanics , artificial intelligence , agronomy , biology
This paper considers the adaptiveH ∞control problem for piecewise affine systems (PWS), a novel synthesis framework is presented based on the piecewise quadratic Lyapunov function (PQLF) instead of the common quadratic Lyapunov function to achieve the less conservatism. First, by designing the projection‐type piecewise adaptive law, the problem of the adaptiveH ∞control of PWS can be reduced to theH ∞control problem of augmented piecewise systems. Then, we construct the piecewise affine control law for augmented piecewise systems in such a way that the PQLF can be employed to establish the stability andH ∞performance. In particular, the Reciprocal Projection Lemma is employed to formulate the synthesis condition as linear matrix inequalities (LMIs), which enables the proposed PQLF approach to be numerically solvable. Finally, an engineering example is shown to illustrate the synthesis results.