Application of global searching algorithms for nonlinear control system designing

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Bilinear Matrix Inequality (BMI), an extension of LMI, is attracting a considerable attention as a powerful tool for designing nonlinear control systems and robust control systems with structured uncertainties.As opposed to LMI, BMI is non-convex and its computation is usually very difficult. Therefore, to find algorithms with rapid convergence with guarantying global optimality is extremely important. For some BMIs, however, there are problems for which long computational time is unavoidable no matter what algorithm is used. In such a case, admitting some conservatism, to use LMI algorithm after converting BMI into LMI is very practical.Standing on the above viewpoint, the following studies are carried out. (i) Extension of LMI technique. (ii) Reduction of BMI into LMI. (iii) Derivation of BMI solving algorithms. (iv) Applications to automobile control systems.The following results are obtained. A new LMI algorithm has been derived for HィイD2∞ィエD2 control problem for descriptor systems. Also, HィイD2∞ィエD2 control problems with time-domain constraints and multi-rate sampled data HィイD2∞ィエD2 control problems have been solved within LMIs. Concerning to the reduction of BMI into LMI, an algorithm has been proposed for parameterized LMI (PLMI) problems. For BMI, observing that BMi has a structure of d.c. constraints (difference of convex functions), a new branch and bound algorithm has been proposed. Finally these results have been applied to automobile controls.