Scalar Criteria Research Articles

Overdamped and Underdamped Linear Dynamical Systems

Conditions are given for underdamped or overdamped linear dynamical systems in terms of loop matrix parameters, (√( C) R√( C)g,g) 2 ≷ 4(√( C) L√( C)g,g) for all [boxV]g[boxV] = 1, g ∈ H. These criteria are looked upon as natural generalizations of the elementary one-loop RLC series scalar criteria ( R/2 L) 2 ≷ 1/ LC, when written in the more suggestive form: (√( C) R√( C)) 2 ≷ 4√( C) L√( C). A simplified test for determining dynamical systems with all complex natural modes or all real modes are presented with additional comments.

On the optimization of vector-valued performance criteria

This note presents necessary and sufficient conditions for the existence of superior solutions to optimization problems having vector-valued performance criteria. It is further shown that, when a superior solution exists, it can be found by optimization of scalar performance criteria.