Qualitative analysis of motion properties of semistate models of large-scale systems

This paper studies the behavior of motions of large-scale (LS) semistate systems (SSS) governed by P_i(t)x_i=M_i(t,x_i)x_i+f_i(t)+h_i(t, x), i=1,2,..., s, =(x₁^Tx₂^T⋯x_s^T)^T, where matrices P_i(t) are singular. Using Lyapunov's approach and the tools for LS system analysis, a variant of attractivity and ultimate boundedness of appropriate time-variable sets are investigated. The results are based on a specific choice of the aggregate functions. It is assumed that the reduction of equations to a normal form of lower order is inconvenient. The aggregation-decomposition approach used in this paper reduces the dimensionality of an aggregate matrix of the system to the number of its systems. Motion properties of LS systems are deduced from the properties of its isolated subsystems, the character of interconnections, and the conditions imposed on the system aggregate matrix. Sufficient algebraic conditions for the above-mentioned motion properties are developed.