Analysis of stability robustness for linear time invariant singular control systems

Abstract

Singular systems are those the dynamics of which is governed by a mixture Of algebraic and differential equations. In that sense the algebraic equations represent the constraints to the solution of the differential part. These systems are also known as descriptor, semi-state and generalized systems. They appear as a linear approximation of systems models, or linear system models in many applications such as electrical networks, aircraft dynamics, neutral delay systems, large-scale systems, interconnected systems economics, optimization problems, feedback systems, robotics, etc. The basic dynamic analysis in time domain is devoted to the question of stability in the sense of Lyapunov as well as in the sense of finite time stability. Besides that, it is of particular interest to maintain the systems characteristics under the action of undesirable perturbations. This question is in the connection with the problems treated well by the modern concept of stability robustness within the area of control engineering.