Rifat Sipahi

Bio: Rifat Sipahi is an academic researcher from Northeastern University. The author has contributed to research in topics: LTI system theory & Control theory. The author has an hindex of 31, co-authored 162 publications receiving 3828 citations. Previous affiliations of Rifat Sipahi include University of Connecticut & University of South Florida.

An exact method for the stability analysis of time-delayed linear time-invariant (LTI) systems

Abstract: A general class of linear time invariant systems with time delay is studied. Recently, they attracted considerable interest in the systems and control community. The complexity arises due to the exponential type transcendental terms in their characteristic equation. The transcendentality brings infinitely many characteristic roots, which are cumbersome to elaborate as evident from the literature. A number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay. This study offers an exact, structured and robust methodology to bring a closure to the question at hand. Ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions (pockets) in the domain of time delay, but it also declares the number of unstable characteristic roots at any given pocket. The method starts with the determination of all possible purely imaginary (resonant) characteristic roots for any positive time delay. To achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation. It is proven that the number of such resonant roots for a given dynamics is finite. Each one of these roots is created by infinitely many time delays, which are periodically distributed. An interesting property is also claimed next, that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency. These two unique findings facilitate a simple and practical stability method, which is the highlight of the work.

Stability and Stabilization of Systems with Time Delay

Abstract: Time-delays are important components of many dynamical systems that describe coupling or interconnection between dynamics, propagation, or transport phenomena in shared environments, in heredity, and in competition in population dynamics. This monograph addresses the problem of stability analysis and the stabilisation of dynamical systems subjected to time-delays. It presents a wide and self-contained panorama of analytical methods and computational algorithms using a unified eigenvalue-based approach illustrated by examples and applications in electrical and mechanical engineering, biology, and complex network analysis.

Stability Robustness Analysis of Multiple Time- Delayed Systems Using “Building Block” Concept

Abstract: An intriguing perspective is presented in studying the stability robustness of systems with multiple independent and uncertain delays. It is based on a holographic mapping, which is implemented over the domain of the delays. This mapping considerably alleviates the problem, which is otherwise known to be notoriously complex. It creates a dramatic reduction in the dimension of the problem from infinity to manageably small number. Ultimately the process is reduced to studying the problem within a finite dimensional cube with edges of length 2pi in the new domain, what we call the building block. In essence, the mapping collapses the entire set of potential stability switching points onto a small (upperbounded) number of building hypersurfaces. We further demonstrate that these building hypersurfaces can be implicitly defined and they are completely isolated within the above mentioned cube. It is also shown that the exhaustive detection of these building hypersurfaces is necessary and sufficient in order to arrive at the complete stability robustness picture we seek. As a consequence, this concept yields a very practical and efficient procedure for the stability assessment of such systems. This novel perspective serves very well for the preparatory steps of the authors' earlier contribution in the area, cluster treatment of characteristic roots (CTCR). We elaborate on this combination, which forms the main contribution of the paper. Several example case studies are also provided

Stability of Traffic Flow Behavior with Distributed Delays Modeling the Memory Effects of the Drivers

Abstract: Stability analysis of a single-lane microscopic car-following model is studied analytically from the perspective of delayed reactions of human drivers. In the literature, the delayed reactions of the drivers are modeled with discrete delays, which assume that drivers make their control decisions based on the stimuli they receive from a point of time in the history. We improve this model by introducing a distribution of delays, which assumes that the control actions are based on information distributed over an interval of time in history. Such an assumption is more realistic, as it takes into consideration the memory capabilities of the drivers and the inevitable heterogeneity of their delay times. We calculate exact stability regions in the parameter space of some realistic delay distributions. Case studies are provided demonstrating the application of the results.

Free-Matrix-Based Integral Inequality for Stability Analysis of Systems With Time-Varying Delay

Abstract: The free-weighting matrix and integral-inequality methods are widely used to derive delay-dependent criteria for the stability analysis of time-varying-delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms. This technical note presents a new integral inequality, called a free-matrix-based integral inequality, that further reduces the conservativeness in those methods. It includes well-known integral inequalities as special cases. Using it to investigate the stability of systems with time-varying delays yields less conservative delay-dependent stability criteria, which are given in terms of linear matrix inequalities. Two numerical examples demonstrate the effectiveness and superiority of the method.

Foundations and Challenges of Low-Inertia Systems (Invited Paper)

Abstract: The electric power system is currently undergoing a period of unprecedented changes. Environmental and sustainability concerns lead to replacement of a significant share of conventional fossil fuel-based power plants with renewable energy resources. This transition involves the major challenge of substituting synchronous machines and their well-known dynamics and controllers with power electronics-interfaced generation whose regulation and interaction with the rest of the system is yet to be fully understood. In this article, we review the challenges of such low-inertia power systems, and survey the solutions that have been put forward thus far. We strive to concisely summarize the laid-out scientific foundations as well as the practical experiences of industrial and academic demonstration projects. We touch upon the topics of power system stability, modeling, and control, and we particularly focus on the role of frequency, inertia, as well as control of power converters and from the demand-side.