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The celebrated Kalman–Yakubovič–Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality, and has played one of the most fundamental roles in systems and control theory. This paper first develops a necessary and sufficient condition for an -procedure to be lossless, and uses the result to(More)
In this paper, we derive graphical and analytic criteria for the existence of periodic oscillations in large-scale cyclic gene regulatory networks, and present quantitative biological insight based on the analytic result. Based on the Poincaré-Bendixson theorem for cyclic systems, it is first shown that local instability of an equilibrium point implies the(More)
In the current study of robust stability of infinite-dimensional systems, internal exponential stability is not necessarily guaranteed. This paper introduces a new class of impulse responses called R, in which the usual notion of L2-input/output stability guarantees not only external but also internal exponential stability. The result is applied to derive a(More)
This paper addresses the problem of stabilization and output-synchronization for a network of interconnected nonlinear agents, where each agent is assumed to be dissipative with respect to a specified quadratic supply rate which may differ among the agents. Main results concern the characterization and design of the information exchange structure for(More)
This paper develops a state-space theory for the study of linear shift-invariant finite-dimensional hybrid dynamical systems. By hybrid system, we mean an inputoutput operator relating hybrid signals, that is, signals which consist of two parts: a continuous-time part and a discrete-time part. We first introduce the hybrid state-space model and show the(More)
This report presents an algebraic approach to polynomial spectral factorization, an important mathematical tool in signal processing and control. The approach exploits an intriguing relationship between the theory of Gröbner bases and polynomial spectral factorization which can be observed through the sum of roots, and allows us to perform polynomial(More)