On the "adiabatic approximation" for design of control laws for linear, time-varying systems

Control laws are often designed for linear time-varying processes by solving the algebraic Riccati equation for the optimum control law at each instant of time. Such designs may be called "adiabatic approximations." Although they are not optimum, they can result in closed loop systems which perform well. The stability of systems designed using the adiabatic approximation can be assessed by the "second method of Lyapunov." Stability is assured if a readily computed test matrix
F
, which depends on the rate of change of the parameters of the system, is negative-definite.