Optimal Control of a Class of Uncertain Piecewise Linear Systems Based on BMI

The optimal control of uncertain piecewise linear systems is converted to the optimization of upper and lower bounds of the cost function.The optimization of upper bound can be cast as a bilinear matrix inequality(BMI)problem in which the feedback gain is a set of optimization parameters,and a mixed algorithm that combines genetic algorithm and interior point method is designed for the BMI problem.The results from numerical example illustrate the effectiveness of the design and calculation approach for the control law.