In this study, linear matrix inequality (LMI) approaches and multiobjective(MO) evolutionary algorithms are integrated to design controllers. An MO matrixinequality problem (MOMIP) is first defined. A hybrid MO differential evolution(HMODE) algorithm is then developed to solve the MOMIP. The hybrid algorithmcombines deterministic and stochastic searching schemes. In the solvingprocess, the deterministic part aims to exploit the structures of matrixinequalities, and the stochastic part is used to fully explore the decisionvariable space. Simulation results show that the HMODE algorithm can produce anapproximated Pareto front (APF) and Pareto-efficient controllers that stabilisethe associated controlled system. In contrast with single-objective designsusing LMI approaches, the proposed MO methodology can clearly illustrate howthe objectives involved affect each other, that is, a broad perspective onoptimality is provided. This facilitates the selecting process for arepresentative design, and particularly the design that corresponds to anon-dominated vector lying in the knee region of the APF. In addition,controller gains can be readily modified to incorporate the preference or needof a system designer.
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