Finite time stability of continuous time delay systems: Jensen's inequality-based approach

Abstract

In this study, finite-time stability of the linear continuous time-delay systems was investigated. A novel formulation of the Lyapunov-like function was used to develop a new sufficient delay-dependent condition for finite-time stability. The proposed function does not need to be positive-definite in the whole state space, and it does not need to have negative derivatives along the system trajectories. The proposed method was compared with the previously developed and reported methodologies. It was concluded that the stability investigation using the novel condition for stability investigation was less complicated for numerical calculations. Furthermore, it gives comparable results in comparison with the ones obtained with other analyzed conditions, and it provides superior results for some systems.

Improved results on finite time stability of time delay systems: Jensen's inequality-based approach

“…The derived result is based on algebraic inequalities only, which can be solved without using appropriate optimization methods. It has been shown that, under some circumstances, the conditions derived in this study leads to significant improvement in the finite time stability analysis, particularly in comparison with results given in [23], [24] 6. ACKNOWLEDGMENT This work has been supported by the Ministary of Science and Technological Department of Serbia under the Project ON 174 001.…”

Finite-Time Stability Analysis: A Tutorial Survey

“…Theorem 15 (see [40]). System (28) associated with initial condition ( 29) is finite-time stable with respect to (α, β, h) if there exists a positive real number c such that the following conditions are satisfied:…”

“…So, various stability problems for delayed systems have attracted much attention to lots of researchers. Among them, finitetime stability analysis has been of particular interest bringing forth many papers such as [40][41][42].…”