A Priori Estimation of Potential Degeneration of Continuous Multichannel Dynamic Systems

Abstract

The problem of a priory control of potential degeneration of continuous multichannel dynamic systems is considered in the paper. Degeneracy is a property of a system describing operability of a multichannel dynamic system together with the basic properties of stability, reliability and invariance to the changing conditions. An assessment of potential generation of a system and its configuration together with the interconnections and polynomial exogenous signal is proposed. Degeneration process of a multichannel dynamic systems is a process of the rank reducing of the linear operator of the system. This statement is a basic concept of the degeneration factors approach. Algebraic properties of the matrix of the system’s operator is considered, and the matrix is named as the criterion matrix. Degeneration factor is calculated with the singular values of the criterion matrix. The global degeneration factor is conditional number of the criterion matrix of a system. In contrast to previous solutions it is proposed to form the criterion matrix of a system with the resolvent of its state matrix. Deparameterization of the linear algebraic problem is realized by additive decomposition of the output vector of the system by derivatives of the exogenous signal, and the steady-state mode of the system is considered. The procedure of a priori estimation of degeneration of continuous multichannel dynamic systems is proposed. The ways to achieve the required value of degeneration of the criterion matrix of the system with the modal control methods are discussed. The paper is supported with examples.