The State Space and Transfer Function Approaches in Practical Linear Multivariable Systems Design

It is shown that the application of state space formalism to linear multivariable time-invariant system design is inherently very limited for practical use and has led to some naive results. The design based on state space formulation does not cope with the entire problem of practical design and its results are more easily derived by transform methods. Then much greater awareness of practical constraints exists, and therefore it is easier to avoid the unrealistic conclusions often reached by the state space approach. A transfer function formalism is then used to present a procedure for stabilizing a multivariable feedback system with significant plant uncertainty. The method requires shaping the nominal loop functions and decreasing their magnitudes with frequency as rapidly as possible such that the system is stable over the range of plant uncertainty. An illustrative example is presented.