Improved delay-range-dependent stability criteria for linear systems with time-varying delays

New Stability Criteria for Linear Systems with Interval Time-varying State Delays

“…For the convenience of readers, we have attempted to use similar notations of [14]. Here, 9 ( 1,...,9) …”

“…In [12], some tripleintegral terms in the Lyapunov-Krasovskii functional were proposed to reduce conservatism of the stability criteria. Based on the triple-integral terms in the LyapunovKrasovskii functional, new delay-range-dependent stability criteria for linear systems with interval time-varying delays were reported in [14]. However, this method has much room for further improvement.…”

“…Unlike the proposed Lyapunov-Krasovskii functional in [14], new Lyapunov-Krasovskii functionals such as ( ) ∫ augmented vectors, a further improved stability criterion will be proposed. Through two numerical examples treated in [13]− [15], the improvement of our results will be demonstrated.…”

Robust H ∞ state-feedback control for linear systems

“…Using the augmented vector (3.3) with the simplification expression (3.2), system (2.5) is represented as 19) where Υ o is defined in theorem 3.1. Hence, the asymptotic stability condition for system (2.5) is expressed as…”

“…Therefore, it is another important means of reducing conservatism with respect to the precise estimation. Three main approaches are employed: the free-weighting matrix [18,19], the Jensen inequality [20,21] and the convex optimization method, as well as their combinations [22][23][24][25]. However, in recent developments some terms have been neglected due to the derivative of the LKF being estimated, which may lead to conservative conditions.…”