Reachable Set Bounding for a Class of Nonlinear Time-Varying Systems with Delay

We investigate the problem of reachable set bounding for a class of continuous-time and discrete-time nonlinear time-varying systems with time-varying delay. Unlike some preceding works, the involved disturbance input and time-varying delay are not assumed to be bounded. By employing an approach which does not involve the conventional Lyapunov-Krasovskii functional, new conditions are proposed such that all the state trajectories of the system converge asymptotically within a ball. Two illustrative examples are also given to show the effectiveness of the obtained results.

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Reachable Set Estimation for Discrete-Time Systems with Interval Time-Varying Delays and Bounded Disturbances

Journal of Control Science and Engineering ◽

10.1155/2016/5214147 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7 ◽

Cited By ~ 3

Author(s):

Jiemei Zhao ◽

Yin Sheng

Keyword(s):

Discrete Time ◽

Reachable Set ◽

Time Varying ◽

Time Varying Delay ◽

Set Estimation ◽

Discrete Time Systems ◽

Bounded Disturbances ◽

Reachable Set Estimation ◽

Time Systems ◽

Varying Delay

The reachable set estimation problem for discrete-time systems with delay-range-dependent and bounded disturbances is investigated. A triple-summation term, the upper bound, and the lower bound of time-varying delay are introduced into the Lyapunov function. In this case, an improved delay-range-dependent criterion is established for the addressed problem by constructing the appropriate Lyapunov functional, which guarantees that the reachable set of discrete-time systems with time-varying delay and bounded peak inputs is contained in the ellipsoid. It is worth mentioning that the initial value of the system does not need to be zero. Then, the reachable set estimation problem for time-delay systems with polytopic uncertainties is investigated. The effectiveness and the reduced conservatism of the derived results are demonstrated by an illustrative example.

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Further Results on Reachable Set Bounding for Discrete-Time System with Time-Varying Delay and Bounded Disturbance Inputs

Complexity ◽

10.1155/2018/9259284 ◽

2018 ◽

Vol 2018 ◽

pp. 1-11

Author(s):

Wei Kang ◽

Hao Chen ◽

Kaibo Shi ◽

Jun Cheng

Keyword(s):

Discrete Time ◽

Sufficient Conditions ◽

Reachable Set ◽

Time Varying ◽

Discrete Time System ◽

Initial State ◽

Time System ◽

Time Varying Delay ◽

Bounded Disturbance ◽

Varying Delay

This paper investigates the problem of reachable set bounding for discrete-time system with time-varying delay and bounded disturbance inputs. Together with a new Lyapunov-Krasovskii functional, discrete Wirtinger-based inequality, and reciprocally convex approach, sufficient conditions are derived to find an ellipsoid to bound the reachable sets of discrete-time delayed system. The main advantage of this paper lies in two aspects: first, the initial state vectors are not necessarily zero; second, the obtained criteria in this paper do not really require all the symmetric matrices involved in the employed Lyapunov-Krasovskii functional to be positive definite. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

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