An Improved Finite-Time Stability and Stabilization of Linear System with Constant Delay

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.

Delay‐dependent conditions for finite time stability of linear time‐varying systems with delay

“…Solving the optimization problem with ε = 0.5, we can get the minimum value of c 2 in Table . It can be concluded that the method in this paper is less conservative than that in .…”

“…Example Considering system with the following parameters : …”

“…Solving the optimization problem (23) with = 0.5, we can get the minimum value of c 2 in Table 1. It can be concluded that the method in this paper is less conservative than that in [37,38,39]. In [31], the time interval [0, T f ] was divided into L segments with the length of each segment h = T f ∕L ≥ 2d.…”

“…Let c 1 = 0.55, T c = 2, δ = 2.1, d = 0.2, Γ( t ) = I 3 , the same with those in . Solving the optimization problem with ε = 0.5, we can get the minimum value of c 2 in Table .…”

New Results for Finite-Time Stability of Discrete-Time Linear Systems with Interval Time-Varying Delay

“…The controller design problem is solved by using the LMIs and the cone complementarity linearization iterative algorithm. In order to get less conservative criteria, a new form of LKL functional with power weighting function is introduced in [18]. In the last few years, with the great development of the switched system theory, the FTS and FTB problems of switched systems with time delay have received increasing attention (see, e.g., [19,20] and the references therein).…”