Suboptimal linear regulators for systems subject to parameter variations

A procedure is developed for designing nearly optimal linear regulators for systems subject to large parameter variations. The technique is applicable to the general multivariable linear system and yields a feedback controller which is relatively easy to implement. Approximate controllers are derived by expanding the gain matrix in a Taylor series expansion in powers of the variable parameter. Gain is adjusted on the basis of measured or estimated values of the parameter. The technique is developed for the case where the cost functional is an explicit function of the variable parameter in order to achieve similar controlled time responses over a wide range of parameter variation. A computational example is presented to illustrate the approach.