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Adaptive H ∞ Control of Piecewise‐Linear Systems with Parametric Uncertainties and External Disturbances
Author(s) -
Liu Kai,
Yao Yu,
Balakrishnan Venkataramanan,
Ma Hongzhong
Publication year - 2013
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.648
Subject(s) - control theory (sociology) , parametric statistics , projection (relational algebra) , piecewise , piecewise linear function , lyapunov function , mathematics , controller (irrigation) , quadratic equation , linear system , adaptive control , mathematical optimization , computer science , nonlinear system , control (management) , algorithm , mathematical analysis , physics , statistics , geometry , quantum mechanics , artificial intelligence , agronomy , biology
In this paper, we study the adaptive H ∞ control problem for piecewise linear systems with parametric uncertainties and external disturbances. Motivated by the vector projection technique and dissipation theory, we propose a piecewise H ∞ controller and its associated projection‐type parameter adaptation law, which are capable of guaranteeing the system stability and minimizing the effect of disturbances. Moreover, the common quadratic Lyapunov function method is used such that all of the synthesis conditions are formulated as linear matrix inequities and thus can be solved efficiently. Finally, a numerical example is provided to illustrate the results.