4,743 research outputs found
The Positive Real Lemma and Construction of All Realizations of Generalized Positive Rational Functions
We here extend the well known Positive Real Lemma (also known as the Kalman-Yakubovich-Popov Lemma) to complex matrix-valued generalized positive rational function, when non-minimal realizations are considered. All state space realizations are partitioned into subsets, each is identified with a set of matrices satisfying the same Lyapunov inclusion. Thus, each subset forms a convex invertible cone, cic in short, and is in fact is replica of all realizations of positive functions of the same dimensions. We then exploit this result to provide an easy construction procedure of all (not necessarily minimal) state space realizations of generalized positive functions. As a by-product, this approach enables us to characterize systems which can be brought, through static output feedback, to be generalized positive
Positive and generalized positive real lemma for slice hyperholomorphic functions
In this paper we prove a quaternionic positive real lemma as well as its
generalized version, in case the associated kernel has negative squares for
slice hyperholomorphic functions. We consider the case of functions with
positive real part in the half space of quaternions with positive real part, as
well as the case of (generalized) Schur functions in the open unit ball
State space formulas for stable rational matrix solutions of a Leech problem
Given stable rational matrix functions and , a procedure is presented
to compute a stable rational matrix solution to the Leech problem
associated with and , that is, and . The solution is given in the form of a state space
realization, where the matrices involved in this realization are computed from
state space realizations of the data functions and .Comment: 25 page
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