Development of Synthesis Methods of Robust Nonlinear Control Systems Based on Numerical Optimization

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The objective of this research is to provide basic theory for robustness analysis, nonlinear system analysis and numerical mythologies to efficiently solve problems in control, aimed to answer stringent requirements in practical control problems to design control systems that work under such as uncertainties and nonlinearities with guarantee of control performance. The outcomes of this research include advanced synthesis methods of gain-scheduled controllers, generalization of stability analysis by using Rantzer's density functions and its application to synthesis of nonlinear control gains, and methods for robust SDPs focusing on numerical verification of strictness of relaxations of robust SDPs