The Stability of Linear Continous Singular and Discrete Descriptor Time Delayed Systems over the Finite Time Interval: An Overview - Part I Continuous Case
Dragutin Debeljković
Sreten Stojanović
Tamara Nestorović
This paper gives sufficient conditions for the
practical and finite time stability of linear singular continuous time
delay systems of the form 
.
When we consider the finite time stability concept, these new delay
independent conditions are derived using an approach based on Lyapunov –
like functions and their properties on the sub-space of consistent
initial conditions. These functions do not need to have: a) properties
of positivity in the whole state space and b) negative derivatives along
the system trajectories.
Considering practical stability, the above mentioned approach is combined and supported by a classical Lyapunov technique to guarantee its attractivity
Key words: linear system, continual system, descriptive system, singular system, time delayed system, discrete system, system stability.