Robust Finite‐Time H ∞ Control of a Class of Disturbed Systems using Lmi‐Based Approach

The paper investigates the observer-based H ∞ synchronization for coronary artery time-delay system under the state immeasurement and external uncertainty. A Luenberger-like state observer, the observation system, is designed to realize the state reconstruction of the master system. Based on the Lyapunov stability theory and Lyapunov-Krasovskii functional (LKF), the observer-based synchronization control condition is derived for a coronary artery system subjected to the external uncertainty bounded by L 2 norm. By introducing the delay-interval bounds and delay-derivative limits in LKF, the time-delays are handled by the delay-range-dependent strategy. The tighter upper bound of inequality can be obtained to reduce the conservation by employing further improved result of Jensen inequality and reciprocally convex approach. Furthermore, a decoupling technique is utilized to render the separate and simple controller and observer synthesis condition, which can be further solved by applying the cone complementary linearization approach respectively. Numerical simulations are listed to exhibit the effectiveness of the presented methodology.

“…Assumption 3. The synchronization error system (7) satisfies the H ∞ performance index with the zero initial condition, if there exists [17,23,24]…”

Section: Assumptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Observer‐Based H_∞ Synchronization Control for Input and Output Time‐Delays Coronary Artery System

Zhao

Zhang

et al. 2018

“…Since many practical applications require that the state does not exceed a certain bound in a fixed time interval, e.g., to avoid saturation or excitation, we focus on the finite-time boundedness analysis in practical consideration. In recent years, many results were reported on finite-time boundedness problems: The relevant concepts of finite-time boundedness [40], finite-time stabilization [41], and finite-time H ∞ performance have been revisited in [42][43][44][45]. However, according to the authors knowledge, resilient H ∞ performance for finite-time boundedness of uncertain neural networks have not been investigated yet.…”

Section: Introductionmentioning

confidence: 99%

Robust resilient H_∞ performance for finite‐time boundedness of neutral‐type neural networks with time‐varying delays

Saravanan

Ali

Hong

et al. 2020

This paper discusses the resilient H ∞ performance for finite-time boundedness of neutral-type neural networks with time-varying delays. The presented theoretical analysis allows establishing the finite-time bounded of the real response of a delayed neural networks. In addition, we propose finite-time stability conditions with time-varying delay. By choosing an appropriate Lyapunov-Krasovskii functional, and employing an auxiliary function-based integral inequality and Wirtinger's based integral inequality, the sufficient criteria are derived in terms of linear matrix inequalities. The purpose is to design the system is not only finite-time bounded with a specified decay rate but also satisfies an H ∞ performance requirement. Theoretical results are tested through a numerical example.

“…Nevertheless, in some practical situations we may be more interested in the finite‐time stability, which sustains the trajectories to not exceed a certain threshold during a fixed short time under a given bound on the initial conditions, since most actual networks only act over finite time. The original concept of finite‐time stability is given in for a class of integer‐order differential systems, and then has been extensively investigated for some kind of integer‐order systems by many researchers . As an extension, research about the finite‐time stability could also be carried out on fractional‐order systems.…”

Section: Introductionmentioning

confidence: 99%

Finite‐Time Guaranteed Cost Control of Caputo Fractional‐Order Neural Networks

Thuận

Binh

Huong

2018

In this paper, we investigate the problem of finite‐time guaranteed cost control of uncertain fractional‐order neural networks. Firstly, a new cost function is defined. Then, by using linear matrix inequalities (LMIs) approach, some new sufficient conditions for the design of a state feedback controller which makes the closed‐loop systems finite‐time stable and guarantees an adequate cost level of performance are derived. These conditions are in the form of linear matrix inequalities, which therefore can be efficiently solved by using existing convex algorithms. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.