Abstract
This paper concerns with the stability of the linear multi-input-output optimal tracking system (Sc*)1), when the open loop gain (μ) of a process changes. Roughly speaking, the following are proved.
(1) Any Sc* remains stable when μ increases.
(2) If the determinant (ρ) of the weighting matrix of the inputs in the quadratic performance function is very small, almost all the resulting Sc* become unstable, when μ decreases.
The above second statement suggests a new term called the conditional stability. It implies that Sc* should not be designed with too small ρ So, this paper also proposes an algorithm to choose proper ρ, considering the degree of stability. The algorithm is very important because it paves the way for systematical determination of the weighting matrices in the quadratic performance function, which are now determined by trial and error.
An example demonstrates an application of the above mentioned theorems and algorithm.
