This paper focuses on the synthesis of well-conditioned rnultivariable robust controllers for a broad class of multi-input multi-output two-time-scale nonlinear systems with time-varying uncertain variables, modeled within the framework of singular perturbations. The proposed controller stabilizes the fast dynamics, guarantees boundedness of trajectories, and ensures that the ultimate discrepan...

The robust stability problem of continuous-time singular systems with multiple state delays and bounded parametric uncertainties is considered. Both commensurate and non-commensurate delays are investigated. On the basis of the linear fractional transformations (LFTs) framework and -analysis, a systematic approach is derived to convert the robustness problem to a robust nonsingularity problem. ...

We present a direct method of calculation of the multifractal spectrum from the wavelet decomposition. Information pertinent to singular structures in time series is captured by the WTMM method and the local effective Hölder exponent is evaluated locally for each singular point of the time series. The direct multifractal spectrum is obtained from the scaling of the histograms of the local effec...

This contribution considers the guaranteed cost control for a class of linear uncertain time-delay switched singular systems under arbitrary switching laws with a given quadratic performance index. Based on a Lyapunov function approach and a linear matrix inequality (LMI) technique, a sufficient condition on the existence of guaranteed cost state feedback controllers is derived, which ensures t...

A new idea was proposed to find out the stability and root location of two dimensional linear time invariant discrete system (LTIDS) for real coefficient polynomials. For determining stability the sign criterion is synthesized from the jury’s method for stability which is derived from the characteristic polynomial coefficients of the discrete system. The number of roots lying inside or outside ...

Order-reduction techniques based on system balancing are developed for linear discrete systems using the method of singular perturbations. The generalized residualization technique is introduced with three variants as improved tools for orderreduction at low and medium frequencies. The newly introduced techniques have the same theoretical upper error bound with respect to the H∞ norm of the red...

The stability of a nonlinear stochastic dynamic system with singular perturbations is considered. Based on the notion of stochastic input-to-state stability and using time scale decomposition, a result of the total stability type is obtained, i.e. if the fast subsystem and the slow subsystem are both input-to-state stable with respect to disturbances, then this property continues to hold for th...

A delay-vector phase space reconstruction in which the delay time satisfies a minimum redundan~ criterion is compared with a reconstruction obtained using a singular system approach, Minimum redundancy produces the better reconstruction. The reconstructions are compared using a distortion functional .~ which measures how well the location of a point in the original phase space can be determ~i~e...

This paper considers the identiiability of state space models for a system that is expressed as a linear fractional transformation (LFT): a constant matrix (containing identiied parameters) in feedback with a nite-dimensional, block-diagonal (\structured") linear operator. This model structure can represent linear time-invariant, linear parameter-varying, uncertain, and multidimensional systems...

Abstract-Relaxation oscillations exhibiting more than one time scale arise naturally from many physical systems. When relaxation oscillators are coupled in a way that resembles chemical synapses, we propose a fast method to numerically integrate such networks. The numerical technique, called the singular limit method, is derived from analysis of relaxation oscillations in the singular limit. In...