Exponential stability for continuous-time singular systems with multiple time delays

In recent years, time-delay systems have been an active area of research (see, e.g., [1-9]). This is due to theoretical interests as well as to a powerful tool for practical system analysis and control design, since delays are often encountered in various engineering systems, such as the turbojet engine, rolling mill, manual control, microwave oscillator, chemical engineering systems, ship stabilization, and systems with lossless transmission lines. Frequently, it is a source of the generation of oscillation and a source of instability in many systems. On the other hand, singular systems with or without time delay have been extensively studied in recent years (see, e.g., [10-17] and the references therein). Many problems can be modeled by such systems, such as electrical circuits, power systems, robotics, population growth models, singularly perturbed systems, constrained control problem, interconnected systems, boundary control system, optimal control problem, and chemical processes [17]. In particular, there are three main characters in singular time-delay systems.. The first is that the characteristic equation of such, systems has infinitely many solutions, hence it is difficult to check the stability of such systems. The second is that impulses may happen in the solutions of such systems, and the third is that, the solution of such systems for any specified initial conditions may not be unique. In the past, there have been a number of interesting developments in searching the stability criteria for singular systems with time delay, but most were restricted to searching the stability criteria for discrete singular systems with time delay or for continuous second order singular systems with single time delay (see, e.g., [11,13-17]). These motivate us to search a stability criterion under which the global exponential stability of a class of continuous-time singular systems with multiple time delays can be guaranteed.