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

Stability analysis is a prerequisite and essential element of application and implementation processes in electrical and electronic fields [1]−[4]. Because time delays occur in many systems, including networked control systems, chemical processes, transportation systems, and neural networks, the issue of stability analysis for time-delay systems has received considerable attention during the last decade. For details, see [5]−[16] and the references therein. In the field of stability analysis for time-delay systems, a major concern is the enlargement of the feasible region of stability criteria to obtain maximum delay bounds of time delays for guaranteeing system stability in a given condition. Therefore, choosing the Lyapunov-Krasovskii functional and estimating an upper bound of its time derivative play key roles to improve the feasible region of stability criteria. The descriptor system approach, Park's inequality, and free-weight matrix techniques are mainly the utilized methods in the field of delay-dependent stability analysis [7]. Based on the method of [13], the delay partition method [15] was utilized such that the upper bound of the derivative of the Lyapunov-Krasovskii functional could be estimated more tightly without increasing the decision variables. 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. Motivated by the above discussions, we revisit the problem of stability analysis for linear systems with interval time-varying delays treated in [13]−[15]. Unlike the proposed Lyapunov-Krasovskii functional in [14], new Lyapunov-Krasovskii functionals such as