Abstract
When it is desired, frequently from the practical engineering standpoints, to design an output feedback gain matrix of linear multivariable control system which makes the closed loop most stable (optimum), it is insufficient that the resultant system satisfies only the Routh-Hurwitz stability condition.
In this paper we do not take the above problem as the quantitative optimization problem so as to minimize the conventional cost functional, but as the qualitative optimization problem in the sense that the total energy with respect to the free system can be made to die out most rapidly. We develop a procedure for the determination of output linear control law which needs no assumption on the initial states.
Firstly, supposing that the existence of energy function E{x(F, t), F} we introduce the concept of the degree of disappearance of that function, that is, Σ(F), where ∧(F)=Σ-1(F) can be interpreted as the largest time constant of all the state space and may be regarded as a figure of merit of the system. Secondly, the algebraic necessary conditions are found for an F*=-u/y that maximizes Σ(F), or equivalently minimizes ∧(F). In addtion, an algorithm for computing F* is shown and finally two-and three-order control systems are analyzed.
