Search

The stability of linear time invariant (LTI) systems with independent multiple time delays and the cluster treatment of characteristic roots (CTCR) paradigm are investigated from a new perspective. It is known that for such systems, all the imaginary characteristic roots can be detected completely on a small set of hypersurfaces in the domain of the delays (Sipahi and Olgac, 2006a). They are called kernel hypersurfaces (KH). The complete description of KH is the only prerequisite for the CTCR stability assessment procedure. As the number of delays increases, however, their evaluation becomes infeasible. Instead, we present a procedure to extract the 2-D cross-sections of these hypersurfaces in the domain of any two of the delays by fixing the remaining delays. In the 2-delay domain of interest, the exact upper and lower bounds of the imaginary spectra are determined. For this, a combination of half-angle tangent representation of the characteristic equation and the Dixon resultant theory is used as the main contributions of this paper. The complete KH are obtained by sweeping the root crossing frequency in this interval. Using this knowledge CTCR creates the cross-section of the stability map in the domain of the two arbitrarily selected delays. We demonstrate the effectiveness of this methodology over an example case study with three independent delays and two commensurate ones. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new method for assessing the bounded input bounded output stability of a class of fractional delay systems with commensurate orders and multiple commensurate delays of retarded type. In the proposed method, first, by mapping the principal sheet of the Riemann surface and a pseudo-delay transformation, an auxiliary polynomial is generated. Then, this auxiliary polynomial is employed to find roots of the characteristic equation on the imaginary axis. The properties of the root path close to these roots are used to identify intervals of delay values, in which the system is stable. The obtained results are illustrated via some numerical examples. [Copyright &y& Elsevier]

Abstract: This paper studies control problems for discrete-time single-input linear time-invariant plants when controlled over a signal-to-noise ratio (SNR) constrained channel. Our focus is on the performance limitations in an architecture that uses channel feedback. We explicitly characterize the interplay between stabilization, optimal performance, and SNR constraints, highlighting the way in which plant dynamical features affect the best achievable performance. We also apply our results to the study of networked control systems where communication takes place over a power constrained erasure channel. In that scenario, we first show that stabilization problems, and problems involving stationary second-order moments, can be dealt with by focusing on a related SNR constrained networked situation. This observation allows one to obtain results valid in the alternative scenario as corollaries of the results obtained when a single SNR constraint is present. [Copyright &y& Elsevier]