| Time-delay singular systems have been used to represent many practical systems, including aircraft, chemical processes, lossless transmission lines, etc. Therefore, more attention has been paid to study the solution behavior, analysis and control of this class of systems. However, most of the results presented in the literature tackled the case of constant time delays. The objective of this research is to deal with the analysis and synthesis of the continuous-time singular systems with time-varying delays.;For the stability problem, delay-dependent stability conditions for this class of systems are developed. Then, delay-range-dependent exponential stability conditions are also developed. Moreover, an estimate of the convergence rate of the state is presented. This result is generalized to the case of multiple time-varying delays. Also, an explicit expression of the algebraic variables in term of the initial condition and the fast variables is given.;For the synthesis problem, state feedback stabilizing controller is considered. H∞ state feedback controller is also considered. Then, static output feedback controller is considered for the time-delay singular system with saturating controllers and input delays.;The proposed results on analysis and synthesis are based on Lyapunov-Krasovskii approach, linear and bilinear matrix inequality techniques and graph theory. The free solver SEDUMI is used to solve the convex optimization problems while PENBMI is used to solve the BMI problems. YALMIP is used as an interface in both cases. Some numerical examples are presented to show the effectiveness of the proposed results.;For the solution behavior, existence and uniqueness of solution for this class of systems are discussed. Impulsive behavior of its solutions is also discussed and conditions for smooth solutions are presented. The problem of compatible initial conditions is also presented. |
