Decoupling multivariable systems by state feedback: sensitivity considerations

The paper considers the effect of parameter variations in a linear, time-invariant multivariable system x=Ax + Bu, y=Cx which can be decoupled into noninteracting single-input/single-output subsystems by state-variable feedback. Variations in the elements of the plant state matrix may cause the decoupled system either to (a) remain decoupled with altered subsystem transfer functions, (b) become recoupled with the subsystem transfer functions unaltered, or (c) become recoupled with altered subsystem transfer functions. For problems in categories (a) and (b), design methods are presented for selecting the decoupled-subsystem pole locations, such that the system performance has a specified low sensitivity to these parameter variations. The problems considered are those in which only elements of the state matrix A are subject to variations, and which result in a nonnegative matrix P which is the solution of a Lyapunov matrix equation.