Hyper-positive real, matrix-valued, rational functions are associated with absolute stability (the Lurie problem). Here, quantitative subsets of functions, related through nested inclusions, introduced. Structurally, this family turns out to be matrix-convex and closed under inversion. A state-space characterization these a corresponding Kalman-Yakubovich-Popov Lemma, is given. Technically, the...

Trilateral haptic systems can be modeled as threeport networks. Analysis of coupled stability of a three-port network can be accomplished in either the passivity or the absolute stability frameworks assuming all three ports are connected to passive but otherwise unknown terminations. This paper first introduces our recent results in terms of extending Raisbecks passivity criterion and Llewellyn...

This paper is concerned with the problem of synthesis of (passive) mechanical one-port networks. One of the main contributions of this paper is the introduction of a device, which will be called the inerter, which is the true network dual of the spring. This contrasts with the mass element which, by definition, always has one terminal connected to ground. The inerter allows electrical circuits ...

The bounded-real and positive-real lemmas solve two important linear-quadratic optimal control problems related to the concepts of non-expansive and passive systems, respectively. The lemmas assume controllability, yet a non-expansive or passive system can be uncontrollable. In this paper, we solve these optimal control problems without assuming controllability. We obtain necessary and sufficie...

Abslrocr -Suppose that a rational function Z ( s ) is defined by a Laurent .series, the coefficients of which are known. Several criteria are given in terms of these coefficients (the Markov parameters of Z(s)) to ensure that Re Z ( j w ) > 0 for all red w. The criteria are defined by using a Cauchy index formulation of the ratio of two rational functions, and they are of three types-involving ...

In this paper, we first give a description of a surjective unit-preserving real-linear uniform isometry $ T : A longrightarrow B$,  where $ A $ and $ B $ are complex function spaces on compact Hausdorff spaces $ X $ and $ Y $, respectively, whenever ${rm ER}left (A, Xright ) = {rm Ch}left (A, Xright )$ and ${rm ER}left (B, Yright ) = {rm Ch}left (B, Yright )$. Next, we give a description of $ T...