Algebraic criterion for absolute stability, optimality and passivity of dynamic systems

The paper presents a solution to the fundamental algebraic problem: find the necessary and sufficient conditions on the coefficients of a real polynomial II(¿) so that it is nonnegative, i.e. II(¿)¿0 for all real ¿¿0 The solution leads to a unique algebraic criterion for absolute stability, optimality and passivity of dynamic systems, which is an alternative to various analytic frequency criteria developed in modern system theory. The algebraic criterion is superior to the analytic criteria since it avoids any graphical construction and is suitable for machine computations.