Distributed nonstationary control system synthesis on a basis of spectral representation in space-time domain

Abstract

It is proposed, based on the spectral representation of the system, to solve the problem of synthesis of a distributed control plant described by PDE, using LMI technique. The system is described by a spectral characteristic vector with the amplitudes of the space-time modes of the Fourier series as components. The spectral characteristic vector is satisfied to an infinite SLAE composed for an initial PDE using the spectral method. For the spectral plant representation in space-time domain the stability, controllability, and observability criterions are formulated. The procedure of control synthesis on the basis of solving of stabilization problem with full information and observation problem is proposed. The expression for time-dependent matrix regulator gain is received.