Brief paper: The decentralized stabilization and control of a class of unknown non-linear time-varying systems

• Authors: E. J. Davison
• Venue: Automatica (Journal of IFAC)
• Year: 1974

The following problem is considered in this paper. Suppose a system S consists of a set of arbitrary interconnected subsystems S"i, i = 1, 2, ..., @W; is it possible to stabilize and satisfactorily control the whole system S by using only local controllers about the individual subsystems without a knowledge of the manner of the actual interconnections of the whole system? Sufficient conditions are obtained for such a result to hold true; in particular it is shown that a system S consisting of a number of subsystems S"i connected in an arbitrary way between themselves with finite gains: S"i: x@?"i = A"i(x"i, t)x"i + b"i(x"i, t)u"i, y"i = c'"i(x"i, t)x"i where A"i and b"i have a particular structure, may be satisfactorily controlled by applying only local controllers C"i about the individual subsystems: C"i: u"i = K'"i(@r)x"i where K"i is a constant gain matrix with the scalar @r appearing as a parameter, provided @r is large enough.