Reachable set estimation for singular systems via state decomposition method

Li, Yang; He, Yong; Lin, Wei-Chih; Wu, Min

doi:10.1016/j.jfranklin.2020.04.031

Cited by 31 publications

(4 citation statements)

References 32 publications

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“…Remark The Jensen inequality, 39 the reciprocally convex matrix inequality 40 and the compound inequality 41 were employed to estimate the LKFs' derivative, which remains room to improve the estimation accuracy. In order to acquire a more accurate closed bounded set, the Wirtinger‐based integral inequality is chosen in Theorem 1.…”

Section: Resultsmentioning

confidence: 99%

Reachable set estimation for discrete‐time systems with hybrid time‐delays

Zhao

2021

Optim Control Appl Methods

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This article investigates the problem of reachable set estimation for linear discrete-time systems (LDSs) with both discrete and distributed delays as well as bounded disturbance inputs. The purpose is to determine a bounded set in which all the LDSs states are in the set. By exploiting Wirtinger-based summation inequality and linear matrix inequalities techniques, a sufficient criterion is established which guarantees the states of LDSs are bounded by the ellipsoid. An improved Lyapunov-Krasovskii (L-K) functional is addressed and the L-K functional matrices are not required all to be positive definite. Finally, the effectiveness and superiority of the proposed methods are substantiated by two numerical examples.

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Section: Resultsmentioning

confidence: 99%

Reachable set estimation for discrete‐time systems with hybrid time‐delays

Zhao

2021

Optim Control Appl Methods

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“…As we all know, the reachable set is a closed set of all states that a dynamic system can reach under bounded disturbance, starting from initial conditions, which is a subject of great research value in robust control theory [1,2]. In recent years, the problem on reachable set estimation (RSE) has been extensively concerned with, and the corresponding studies about RSE have been obtained for various systems, for example, singular systems [3][4][5][6], neural network systems [7][8][9][10], and fuzzy systems [11][12][13][14]. In addition, the RSE has been applied in many practical systems, for example, avoiding unknown collisions [15], recognizing safe regions [16], and tracking control of underwater vehicle [13].…”

Section: Introductionmentioning

confidence: 99%

On reachable set synthesis of delay Markovian jump systems under partially delay‐dependent asynchronous control

Feng

2022

Asian Journal of Control

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This paper pays close attention to the reachable set synthesis problem for discrete‐time delayed Markovian jump systems (DDMJSs) under partially asynchronous control. Different from the traditional controller, a class of partially asynchronous controller is proposed, where delay‐free and delay states are comprised and cannot take place at the same time. In addition, Bernoulli variable is used to describe the probability distribution of the above two kinds of states, and the design of feedback controller is considered. On this basis, the sufficient conditions which the state feedback controller is existent are solved effectively by using linear matrix inequalities (LMIs). Furthermore, the results of reachable set synthesis are extended to the DDMJs with uncertain transition probabilities. Finally, several numerical simulations are given to show the effectiveness of the presented methods.

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“…In the framework of bounded ellipsoids, Lyapunov functions and LMI methods play a fundamental role in study of reachable set. To mention a few results, the reachable set estimation problem for discrete‐time switched systems under arbitrary switching is dealt with based on a relaxed Lyapunov functional in [12], estimating the reachable set for singular systems is studied by constructing an augmented Lyapunov functional in [13], and the Lyapunov functional method with discontinuous multiple integrals is employed to investigate the problem of reachable set estimation for discrete‐time switched linear systems in [14].…”

Section: Introductionmentioning

confidence: 99%

On reachable set problem for impulse switched singular systems with mixed delays

Zhang

Feng

Zhang

2022

IET Control Theory & Appl

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This paper focuses on the reachable set problem for impulse switched singular (ISS) systems with mixed time-varying delays via the Lyapunov theory. To solve the state boundary of system, a real-bounded lemma is developed by analyzing the impulse switching point under bounded disturbance input and initial function. Based on real-bounded lemma and integral inequality technology, a sufficient condition for reachable set of ISS system is established in the form of linear matrix inequalities (LMIs) to ensure that the reachable state of system is limited to a closed bounded set. Simulation results are given to verify the validity of the obtained theoretical results for the reachable state criterion.

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Reachable set estimation for singular systems via state decomposition method

Cited by 31 publications

References 32 publications

Reachable set estimation for discrete‐time systems with hybrid time‐delays

Reachable set estimation for discrete‐time systems with hybrid time‐delays

On reachable set synthesis of delay Markovian jump systems under partially delay‐dependent asynchronous control

On reachable set problem for impulse switched singular systems with mixed delays

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