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This paper studies the problem of finite-time robust stabilization of inertial delayed neural networks with external disturbances. The finite-time stability research of inertial neural networks can be applied to important fields such as secure communication, so it has great significant research value. However, up to now, there are few previous studies on the finite-time stability of inertial neural networks, thus this paper makes up for this gap. Based on the actual communication networks, we improve the model of inertial neural networks, adding uncertainties and external disturbances. Unlike many previous papers based on scalar sign function, this paper introduces vector sign function, combines the constructed Lyapunov function, some inequality conditions, and related lemmas to design two effective controllers composed of U 1 ( t ) and U 2 ( t ) , which can handle uncertainties and external disturbances of the neural networks well, and realize finite-time robust stability of the neural networks with external disturbances. In addition, the theoretical part of this paper estimates an upper bound on the settling time for the system to reach stability. Under the conditions of a certain strategy, we further optimize the extremes of the settling time so that the system reaches stability in a shorter time. Our results improve and extend some recent works. Finally, two examples are given to verify the validity and correctness of the designed controllers by numerical simulations using MATLAB tool.

A translational oscillator with a rotational actuator (TORA) is an underactuated nonlinear mechanical system with two degrees of freedom (DOF). This paper concerns the robust stabilization control problem for the system with multiple external disturbances. First, a disturbance observer is constructed based on the internal nonlinear dynamic behavior of the system. Second, a robust stabilization controller is designed by the estimated disturbances and the fixed-time sliding mode control method. The controller realizes the global robust stabilization control objective of the TORA system, and the stability of both disturbance observer and robust closed-loop control system are analyzed using the Lyapunov theorem. Finally, the effectiveness of the theoretical results are verified by numerical experiments.

In this paper, by introducing a new general state-space form for uncertain linear time-invariant fractional-order systems subjected to interval and polytopic uncertainties, two problems including robust stability analysis and robust stabilization of the presented systems are investigated. Subsequently, two sufficient conditions in terms of several linear matrix inequalities for the problems mentioned are concluded as two separate theorems. It is assumed that the fractional order α is a known constant belonging to 0 < α < 1 . Simulation results of two different numerical examples demonstrate that the provided sufficient conditions are applicable and effective for tackling robust stability and stabilization problems.

By introducing some slack matrices, this paper proposes less conservative robust stabilization conditions for the polynomial fuzzy system with parametric uncertainties. In the proposed methods, no inverse polynomial matrices are chosen as the decision variables so that each element of the gain and the Lyapunov matrices can be guaranteed to strictly be a polynomial function. Therefore, the hardware implementation cost of operating the proposed controller is reduced because no rational functions need to be computed. Moreover, the fuzzy controllers are designed under perfect and imperfect premise matching conditions to enhance the design flexibility. Finally, some numerical examples are given to demonstrate the effectiveness of the proposed methods.

Low‐frequency inter‐area oscillation is one of the major problems to transfer the bulk power from one area to another area in an interconnected large power system. A wide‐area signal‐based controller is more effective to improve the damping of the inter‐area oscillation than a local area signal‐based controller. A wide‐area measurement system makes it easier to transmit the wide‐area signal through the communication system from the remote location to the controller site. However, the involvement of the unavoidable time delay in the wide‐area signal transmission from a remote area to a controller site is to possess a great deal of challenge to design a damping controller. In this study, a unified Smith predictor (USP)‐based loop shaping controller is designed to handle the negative effect of the delay using the wide‐area signal. The robust stabilization normalised co‐prime factor problem is converted into a generalised H ∞ optimisation problem for additional pole placement constraints. The performances of the USP‐based loop‐shaping H ∞ controller are compared with the USP‐based H ∞ controller. From the obtained results, it is verified that the proposed controller gives an excellent damping performance and handles the effect of time delay.

This paper investigates the finite-time and fixed-time stabilization (FFTS) of switched systems with discontinuous dynamics, external disturbances and delays. Firstly, a new parameterized discontinuous stabilizer is designed to ensure the FFTS of switched discontinuous systems in the sense of Filippov solutions. Secondly, a detailed analysis is provided on how to regulate the power parameters to determine the settling time is finite or fixed. Thirdly, a new adaptive controller is further designed to stabilize the considered system in a finite time, and the corresponding settling time is estimated as well. Finally, two examples are given to demonstrate the efficiency of the proposed method.

This paper investigates the robust stability and stabilization of networked evolutionary games (NEGs) with time delays. First, a mathematical model is presented to describe the dynamics of NEG with time-varying delays and disturbances. Second, an auxiliary system is constructed using the semi-tensor product of matrices and a dimension augmenting technique. Then, a verification condition of robust stability is derived. Third, in order to stabilize NEG to the Nash equilibrium, the robust stability problem is transformed into the robust stabilization problem. Moreover, an algorithm is proposed to design the stabilization controller. Finally, the validity of the results is verified by an example.

The paper proposes a method for solving the Brockett problem based on the synthesis of robust modal control for systems with non-stationary parameters, which does not require complex adaptation algorithms that involve the introduction of a variable regulator matrix. A transition to the task of synthesizing the regulator is shown, using a certain optimality criterion with limitations, which provides similar values to those of the regulator coefficients. A practical numerical example of setting and solving this problem is presented, which confirms the effectiveness of the proposed method. To illustrate the results obtained, a root travel time curve was constructed for two systems: robust and non-robust.

The robust stabilization problem with respect to both dynamic and parametric uncertainty for linear deterministic systems is analyzed in the present article. The robust design methods consider either the dynamic modelling in frequency domain of the uncertainty or, its parametric representation in the state space realisation. Suitable analysis approaches for parametric uncertainty modelling are provided by Kharitonov and Edge-type theorems. Under some specific assumptions, these methods allow to determine the whole admissible domain of the uncertain parameters for which a system is stable. It shall describe a method that combines the advantages of the control techniques with ones given by the polytopic representation of parametric uncertainty. A modified ∞ loop-shaping approach allowing to solve control problems in which robust stabilization, sensitivity reduction, and model following design objectives are formulated is presented and it allows to handle tracking design specifications. The modified loop-shaping procedure allows to design a controller that provides a) robust stability with respect to the normalized left coprime factorization (NLCF); b) reduced sensitivity with respect to output disturbance on a specified range of frequencies, and c) tracking of the output of a given ideal model. The article is finished with a case study in which a two degrees-of-freedom control system with respect to the pitch angle for the longitudinal dynamics of a UAV (ARCHER V1.7) is designed using the modified ∞ loop-shaping procedure.

Given a nominal plant, together with a fixed neighborhood of this plant, the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood (in an appropriate sense). If a controller achieves this design objective, we say that it robustly stabilizes the nominal plant. In this paper we formulate the robust stabilization problem in a behavioral framework, with control as interconnection. We also formulate a relevant behavioral H∞ synthesis problem, which will be instrumental in solving the robust stabilization problem. We use both rational and polynomial representations for the behaviors under consideration. Necessary and sufficient conditions for the existence of robustly stabilizing controllers are obtained using the theory of dissipative systems. We will also find the optimal stability radius, i.e., the smallest upper bound on the radii of the neighborhoods for which there exists a robustly stabilizing controller. This smallest upper bound is expressed in terms of certain storage functions associated with nominal control system. [PUBLICATION ABSTRACT]