Reachable set bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov–Krasovskii functional approach

Zuo, Zhiqiang; Ho, Daniel W. C.; Wang, Yijing

doi:10.1016/j.automatica.2010.02.022

Cited by 105 publications

(94 citation statements)

References 9 publications

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“…. , n, our approach is similar to the ones proposed in [6][7][8][9][10][11]. The reachable set (3) of system (1) is then bounded by ellipsoid ε(P , 1), whose volume, as suggested therein, can be minimized by solving the following optimization problem for a scalar δ > 0:…”

Section: Remark 32mentioning

confidence: 98%

“…Based on the modified Lyapunov-Krasovskii functional, an improved condition for the reachable set bounding problem is proposed in [7] for time-delayed linear systems with bounded peak disturbances. A maximal Lyapunov-Krasovskii functional approach is used to derive conditions for reachable set bounding of linear systems with polytopic uncertainties and non-differential time-varying delays [8]. A further result for uncertain polytopic systems with interval time-varying delay is reported in [10].…”

Section: Introductionmentioning

confidence: 99%

“…To obtain the available information about the maximum allowable time delay required to guarantee stability, extensive research has focused on determining delay-dependent stability or stabilization criteria for these systems. In this context, the problem of reachable set bounding for time-delay systems has received considerable attention in recent years, see, e.g., [5][6][7][8][9][10][11] and references therein. A reachable set is defined as a set of all the states that can be reached from the origin, in finite time, by input with bounded peak value and subject to uncertainties.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

That

Nam

2012

J Optim Theory Appl

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This paper addresses the problem of reachable set bounding for linear discrete-time systems that are subject to state delay and bounded disturbances. Based on the Lyapunov method, a sufficient condition for the existence of ellipsoid-based bounds of reachable sets of a linear uncertain discrete system is derived in terms of matrix inequalities. Here, a new idea is to minimize the projection distances of the ellipsoids on each axis with different exponential convergence rates, instead of minimization of their radius with a single exponential rate. A smaller bound can thus be obtained from the intersection of these ellipsoids. A numerical example is given to illustrate the effectiveness of the proposed approach.

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Section: Remark 32mentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

That

Nam

2012

J Optim Theory Appl

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“…The problem of reachable set estimation (bounding) for linear systems has been addressed in [1][2][3][4][5][6][7][8][9][10], to name a few. In all of the aforementioned works, the involved system was mainly aimed at linear time invariant systems.…”

Section: Introductionmentioning

confidence: 99%

Reachable Set Estimation for a Class of Nonlinear Time-Varying Systems

Sun

Meng

2017

Complexity

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This paper studies the problem of reachable set estimation for a class of nonlinear time-varying systems with disturbances. New necessary and (or) sufficient conditions are derived for the existence of a ball such that all the solutions of the system converge asymptotically within it. Explicit estimation on the decay rate is also presented. The method used in this paper is motivated by that for positive systems, which is different from the conventional Lyapunov-Krasovskii functional method. A numerical example is given to illustrate the effectiveness of the obtained result.

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“…An improved condition for reachable set bounding for linear systems with delay was proposed in [21] by virtue of a Lyapunov-Krasovskii type functional and the rate of delay. Less conservative estimation results on the reachable set for delayed systems with polytopic uncertainties were established in [22,23] by choosing pointwise maximum Lyapunov functional corresponding to a vertex of the polytope. A delay-partitioning method was applied to study the reachable set bounding problem of delayed systems in [24], which further reduced the conservatism of some existing results.…”

Section: Introductionmentioning

confidence: 99%

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

Zhu

Sun

Meng

2018

Advances in Mathematical Physics

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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 bounding for delayed systems with polytopic uncertainties: The maximal Lyapunov–Krasovskii functional approach

Cited by 105 publications

References 9 publications

Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

Reachable Set Bounding for Linear Discrete-Time Systems with Delays and Bounded Disturbances

Reachable Set Estimation for a Class of Nonlinear Time-Varying Systems

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

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