Numerical Methods for Solving Optimization Problems with Differential Linear Matrix Inequalities

A number of problems for dynamic analysis, phase state estimation, and control synthesis for linear and nonlinear systems with uncertain disturbances can be reduced to optimization problems with differential linear matrix inequalities. The numerical methods are proposed for solving such problems by discretization on the considered interval and reducing to the set of interconnected optimization problems at discrete time moments with constraints in the form of linear matrix inequalities. The proposed methods, in comparison with those existing in the literature, guarantee the fulfillment of the differential constraints and allow one to determine the control gain not only at the sampling points but at all points inside the considered time interval.