Continuous robust system synthesis based on minimization of estimation of the relative intervality of trace of the state matrix

An algorithm for synthesis of robust control system for a continuous plant with uncertain interval parameters is proposed in the paper. A concept of relative intervality of the following interval mathematical objects is used to ensure robustness of the system: a scalar, a vector, a numerical characteristic of matrix namely trace. The problem is solved by the median modal control method taking into account the relative intervality of trace of the system state matrix. The trace of a matrix is the sum of the eigenvalues. The desired relative intervality value of standard system indicators is guaranteed. It is shown that relative intervality of trace of the system state matrix is equal to relative intervality of trace of multiply eigenvalue when the state matrix has one multiple eigenvalue. Relative intervality of trace of the system state matrix is changed by changing its median component. It is realized by introducing feedback on the plant state vector. The obtained results are illustrated by an example.