Operative adjustment of a nonstationary system by a criterion of noninteraction (Q1282566)

The authors consider linear time-varying control systems of the form \[ dx/dt = [A(t) + K(t)]x + [B(t)+N(t)]u(t) \] which can be decomposed into a number of interconnected subsystems. The problem addressed is whether for given \(A\) and \(B\), there exist open loop matrix valued controls \(K\) and \(N\) such that for the resulting system the subsystems are noninteracting (i.e. decoupled) and operator definite (i.e. each subsystem can be expressed by a time-invariant linear system). Three different algorithmic approaches to this problem are given under different structural assumptions on \(A\) and \(B\), where also the robustness under incomplete information is discussed. As an example, a problem of airplane motion control is given.