Abstract
Practical systems in engineering fields often require that values of state variables, during the finite-time interval, must not exceed a certain value when the initial values of state are given. This leads us to investigate the finite-time stability and stabilization of a linear system with a constant time-delay. Sufficient conditions to guarantee the finite-time stability and stabilization are derived by using a new form of Lyapunov-Krasovskii functional and a desired state-feedback controller. These conditions are in the form of LMIs and inequalities. Two numerical examples are given to show the effectiveness of the proposed criteria. Results show that our proposed criteria are less conservative than previous works in terms of versatility of minimum bounds and larger bounds of time-delay.
Highlights
In the past decades, researchers have paid much attention to asymptotic stability which concerns behaviors of state variables over an infinite time interval
One disadvantage of the asymptotic stability behavior is that large values of state variables may present during transient period
The presence of large values should not exceed its limit, for example, the presence of saturations or the excitation of nonlinear dynamics [1, 2]. This leads us to a concept called finite-time stability, introduced back in 1960s. This concept is focusing on the behavior of state variables during the transient period which must not exceed a certain value when the upper bound of initial condition is given
Summary
Researchers have paid much attention to asymptotic stability which concerns behaviors of state variables over an infinite time interval. One disadvantage of the asymptotic stability behavior is that large values of state variables may present during transient period. The presence of large values should not exceed its limit, for example, the presence of saturations or the excitation of nonlinear dynamics [1, 2] This leads us to a concept called finite-time stability, introduced back in 1960s. This concept is focusing on the behavior of state variables during the transient period which must not exceed a certain value when the upper bound of initial condition is given (see [1, 3,4,5]). To illustrate the efficiency of the proposed conditions, two numerical examples are presented at the end
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