Abstract
This paper presents a new guaranteed cost control for exponential stability of a nonlinear system with mixed time-delays in state and feedback control. The considered mixed time-delays are both discrete and distributed time-varying delays, but not necessarily differentiable. The proposed conditions allow us to design the state feedback controllers which stabilize the closed-loop system. By constructing an appropriate Lyapunov–Krasovskii functional, new delay-dependent sufficient conditions for the existence of guaranteed cost control are given in terms of linear matrix inequalities (LMIs). Moreover, we design new quadratic cost functions and minimize their upper bound. Finally, numerical examples are given to illustrate the effectiveness and improvement over some existing results in the literature.
Highlights
Nonlinear systems for modeling the behavior of many engineering systems, such as offshore platforms, earthquake dynamics, electronic circuits, and so on have been widely explored
5 Conclusion and future study In this paper, we have investigated the problem of guaranteed cost control for exponential stability of a nonlinear system with mixed time-varying delays in state and feedback control
The mixed time-varying delays, which consisted of both interval and distributed time-varying delays, were considered without assuming the differentiability of the time-varying delays
Summary
Nonlinear systems for modeling the behavior of many engineering systems, such as offshore platforms, earthquake dynamics, electronic circuits, and so on have been widely explored. The problem of stability of time-delay systems has received considerable attention during the past several decades [8,9,10,11,12,13,14]
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