The nonlinear system considered in this paper consists of two components—a linear system and a time-varying nonlinear element in the feedback connection—and is almost periodic. It is shown using a state-space approach (or Lyapunov approach) that if the well-known circle criterion is satisfied, then there exists an almost periodic solution which is uniformly asymptotically stable in the large. F...

A numerically reliable state space algorithm is proposed for computing normalized coprime factorizations of periodic descriptor systems. A preprocessing step is used in the algorithm to convert the initial problem for possibly non-causal systems into a simpler problem for causal periodic systems. The main computational ingredient here is the computation of a coprime factorization with causal fa...

We propose in this paper a self-referenced method based on asynchronous sampling to monitor the waveform of periodic and quasi-periodic signals, with a low number of samples, typically 214 or lower. It provides a high-resolution representation of the signal under test, representative of the analog intensity signal under test. Additionally, the proposed approach is robust to the timin...

MOTIVATION Periodic patterns in time series resulting from biological experiments are of great interest. The commonly used Fast Fourier Transform (FFT) algorithm is applicable only when data are evenly spaced and when no values are missing, which is not always the case in high-throughput measurements. The choice of statistic to evaluate the significance of the periodic patterns for unevenly spa...

The problem of modeling periodic signals is considered. The approach taken here is motivated by the well known theoretical results on the existence of periodic orbits for Liénard systems and previous results on modeling periodic signals by means of second-order nonlinear ordinary differential equations (ODEs). The approach makes use of the appropriate conditions imposed on the polynomials of th...

Periodic switching of cryptographic keys is commonly employed as a mechanism to enhance the security of encryption methods. In this Letter, cycling chaos, in which orbits of certain coupled iterated maps make periodic excursions between chaotic sets, is proposed as a new encryption approach that combines chaotic behavior with periodic switching of keys. The actual encryption process is similar ...

We propose an elegant and conceptually simple method for computing the periodic solution of three classes of periodic matrix equations | Ric-cati, Lyapunov and Sylvester. Such equations arise naturally in several problems of linear system theory. Our approach is very attractive from a numerical point of view, since it is based on the periodic Schur form of techniques involving unitary (orthogon...

We discuss the numerical solution of the output feedback optimal periodic control problem by using a gradient search based optimization approach. For the evaluation of the cost function and its gradient explicit expressions are derived which involve the numerical solution of a pair of discrete-time periodic Lyapunov equations. Efficient numerically reliable algorithms based on the periodic Schu...

This paper presents an improved method of training for the unvoiced filter that comprises an excitation model, within the framework of parametric speech synthesis based on hidden Markov models. The conventional approach calculates the unvoiced filter response from the differential signal of the residual and voiced excitation estimate. The differential signal, however, includes the error generat...

Thyrotoxic periodic paralysis (TPP) attacks are characterized as recurrent, transient episodes of muscle weakness that range from mild weakness to complete flaccid paralysis. Episodes of weakness are accompanied by hypokalemia, which left untreated can lead to life-threatening arrhythmias (6). In this case study, we followed a patient's potassium levels analyzing how they correlate with electro...