access icon free Exponential stability of impulsive systems with random delays under sampled-data control

© The Institution of Engineering and Technology
Received 29/05/2017, Accepted 03/08/2017, Published 10/08/2017

In this study, the exponential stability problem of impulsive system is investigated via sampled-data control in the presence of random time-varying delays and non-linear perturbations. In particular, the time delays are considered to be randomly time varying and they obey the Bernoulli distributions. The authors' main attention is focused on the design of a sampled-data controller to ensure an exponential stability for the closed-loop system. By extending the first- and second-order reciprocal convex approach, an efficient method called third-order reciprocal convex technique is used to manipulate the main results. Through the construction of a suitable Lyapunov–Krasovskii functional combined with input delay approach and Briat lemma, several delay-dependent sufficient conditions for the concerned system are derived in the form of linear matrix inequalities which can be readily solved by utilising the valid software packages. Some numerical examples are given to illustrate the effectiveness of the developed control technique.

Inspec keywords: convex programming; nonlinear control systems; sampled data systems; Lyapunov methods; time-varying systems; closed loop systems; linear matrix inequalities; delay systems; asymptotic stability; control system synthesis

Other keywords: closed-loop system; Briat lemma; impulsive systems; third-order reciprocal convex technique; linear matrix inequalities; second-order reciprocal convex approach; delay-dependent sufficient conditions; software packages; Lyapunov-Krasovskii functional; exponential stability problem; random time-varying delays; input delay approach; sampled-data control design; nonlinear perturbations; first-order reciprocal convex approach; Bernoulli distributions

Subjects: Discrete control systems; Control system analysis and synthesis methods; Time-varying control systems; Linear algebra (numerical analysis); Stability in control theory; Nonlinear control systems; Distributed parameter control systems; Optimisation techniques

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