Stability Matrix

This book introduces several novel contributions into the current literature. Firstly, given that microgrid topologies are paramount in theoretical analysis, the author has proposed a rigorous method of computing the network’s admittance matrix and developed to facilitate the stability analysis of DC microgrids supplying nonlinear loads. This unique approach enabled the factorisation of the admittance matrix in a particular way that facilitates a rigorous theoretical analysis for deriving the stability conditions.

This book introduces several novel contributions into the current literature. Firstly, given that microgrid topologies are paramount in theoretical analysis, the author has proposed a rigorous method of computing the network’s admittance matrix and developed to facilitate the stability analysis of DC microgrids supplying nonlinear loads. This unique approach enabled the factorisation of the admittance matrix in a particular way that facilitates a rigorous theoretical analysis for deriving the stability conditions.

Frequency Domain Criteria for Absolute Stability focuses on recently-developed methods of delay-integral-quadratic constraints to provide criteria for absolute stability of nonlinear control systems. The known or assumed properties of the system are the basis from which stability criteria are developed. Through these methods, many classical results are naturally extended, particularly to time-periodic but also to nonstationary systems. Mathematical prerequisites including Lebesgue-Stieltjes measures and integration are first explained in an informal style with technically more difficult proofs presented in separate sections that can be omitted without loss of continuity.

This book provides a clear understanding in formulating stability analysis and state feedback control of retarded time delay systems using Lyapunov’s second method in an LMI framework. The chapters offer a clear overview of the evolution of stability analysis in terms of the construction of a Lyapunov functional and use of the integral inequalities in order to reduce the gap of delay upper bound estimate compared to frequency domain method through existing and proposed stability theorems.

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations.