Robust delay-derivative-dependent state-feedback control for a class of continuous-time system with time-varying delays

New optimal analysis method to stability and H∞ performance of varying delayed systems

This work investigates the stability and H_∞ performance of interval time-varying delay systems. The aim is to find new optimal analysis method, which can integrate the constructed Lyapunov-Krasovskii functional (LKF) with estimating technique effectively to reduce the conservatism of the main results. A new augmented vector and LKF with triple integral terms are constructed to establish relationships among different vectors firstly. Then two different integral inequalities are used to show how to integrate constructed LKF with estimating technique effectively to reduce the conservatism of the main criteria. Meanwhile, less conservative criteria are derived compared with some existing results. Numerical examples are also given to show the superiority of the proposed approaches.

Robust H∞ state-feedback control for linear systems

This paper investigates the problem of robust H∞ control for linear systems. First, the state-feedback closed-loop control algorithm is designed. Second, by employing the geometric progression theory, a modified augmented Lyapunov-Krasovskii functional (LKF) with the geometric integral interval is established. Then, parameter uncertainties and the derivative of the delay are flexibly described by introducing the convex combination skill. This technique can eliminate the unnecessary enlargement of the LKF derivative estimation, which gives less conservatism. In addition, the designed controller can ensure that the linear systems are globally asymptotically stable with a guaranteed H∞ performance in the presence of a disturbance input and parameter uncertainties. A liquid monopropellant rocket motor with a pressure feeding system is evaluated in a simulation example. It shows that this proposed state-feedback control approach achieves the expected results for linear systems in the sense of the prescribed H∞ performance.

New H∞ control approaches for interval time-delay systems with disturbances and their applications

In this paper, the H_∞ performance and control problems for linear systems with interval state or input delays and disturbances are investigated. In order to exploit more information on the delay range, the quadruple -integral terms and quadratic forms of triple integrals are introduced into the Lyapunov-Krasovskii functional (LKF). Particularly, an improved integral inequality is developed for estimation of the cross terms in triple-integral type, which displays significant improvement over the Wirtinger inequality. As a result, a less conservative H_∞ performance criterion is derived without requiring many slack variables. Based on the criterion, the H_∞ controller design approaches are obtained. Besides the numerical examples, the applications to the practical systems are also provided to illustrate the effectiveness of the proposed approaches.

Improved stability and stabilization design for networked control systems using new quadruple-integral functionals

This paper investigates stability analysis and stabilization for networked control systems. By a refined delay decomposition approach, slightly different Lyapunov-Krasovskii functionals (LKFs) with quadruple-integral terms and augmented vectors containing triple-integral forms of state are constructed. New integral inequalities are proposed to estimate the cross terms from derivatives of the LKFs, which can be proved to offer tighter bounds than what the Jensen one produces theoretically. Moreover, the non-strictly proper rational functions in deriving process are fully handled via reciprocally convex approach. A state feedback controller design approach is also developed. Numerical examples and applications to practical power and oscillator systems demonstrate the superiority of the proposed criteria in conservatism reduction compared to some existing ones.