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The purpose of this paper is to demonstrate an effectiveness of applying a number of the new methods, proposed in the parametric control theory for testing macroeconomic models for the possibility of their practical application.

Approaches of system analysis on building and calibrating the mathematical models; provisions of the parametric control theory for both numerical testing of the calibrated models for the possibility of their practical application and solving the parametric control problems.

First, one global computable general equilibrium model (CGE model) is built and calibrated. Second, in solving the problem of testing this model for the possibility of its practical application the effectiveness of applying two developed numerical algorithms is demonstrated. These algorithms are for estimating stability indicators and estimating stability (in the sense of the theory of smooth mappings stability) of mappings defined by the model. Third, on the base of the tested CGE model there are given the solution results for a number of the parametric control problems aimed at economic growth and decrease of economic disparities of regions.

By the example of the developed CGE model, it is demonstrated an approach of the parametric control theory for testing macroeconomic models for the possibility of their practical application.

This paper aims to present a theoretical method for analyzing the stability and control of a hingeless helicopter in the presence of windshear.

In this paper, the stability and control of a hingeless helicopter in the presence of windshear are investigated. First, the rotary wing dynamic model considered is the one of flap‐pitch (including the elastic deformation of the control system)‐torsion coupling. The induced velocity nonuniform distribution derived from vortex theory is taken into account. Then, as for atmospheric turbulence, the linear windshear model is used for modeling the variation of wind field. Finally, according to the calculated results of the stability characteristic roots and the control response of the helicopter, the helicopter performance in wind shear field is analyzed, and some conclusions are obtained.

Some useful conclusions are obtained through sample analysis.

Although the analyses for stability and control of a hingeless helicopter in the presence of windshear could be obtained using the current method, the model of complex wind field will still be expected in future studies.

A very useful method for analyzing helicopter stability and control.

The proposed method is valid and available for the analysis of helicopter flight dynamics.

Studies of the hingeless rotor helicopter dynamic stability and control laws are conducted. A new method is given for the calculation of stability and controllability of a helicopter in flight condition with lateral velocity. First, the rotary wing dynamic model considered is the one of flap‐pitch (including the elastic deformation of control system) – torsion coupling. The induced velocity non‐uniform distribution derived from vortex theory is taken into account. Then, according to the established motion model of the helicopter, the effects of induced velocity distribution, flap‐pitch‐torsion coupling and lateral velocity on the stability and controllability of the helicopter are analyzed. Based on the analyses of dynamic stability of the helicopter, the unstable mode and the necessity of installation of stability augmentation system (SAS) are recognized. Finally, the control laws of SAS for helicopter pitching, rolling and yawing motions are presented. After establishing helicopter flight control state equations, the performance analyses and step response simulation for helicopter SAS are carried out.

The paper aims to provide further study on the development and analysis of flight control system for two‐dimensional (2D) differential geometric (DG) guidance and control system based on the application of a set‐point weighting proportional‐integral‐derivative (PID) controller.

The commanded angle‐of‐attack is developed in the time domain using the classical differential geometry theory. Then, a set‐point weighting PID controller is introduced to develop a flight control system so as to form the 2D DG guidance and control system, and the gains of the PID controller are determined by the Ziegler‐Nichols method as well as the Routh‐Hurwitz stability criterion. Finally, the classical frequency method is utilized to study the relative stability and robustness of the designed flight control system.

The results demonstrate that the designed controller yields a fast responding and stable system which is robust to the high frequency parameters variation. Moreover, the DG guidance law is viable and effective in a realistic missile defense engagement.

This paper provides a novel approach on the development of DG guidance and control system associated with its stability analysis.

The purpose of this paper is to discuss the Schur D‐stability and the vertex stability of interval matrices (including point matrix obviously). Some new sufficient conditions (criteria) are proposed which guarantee the interval matrix is Schur D‐stable. This results are shown to be less conservative than those in recent literatures. In addition, two equivalence relations between the Schur D‐stability and the vertex stability of interval matrices will be proposed and a new Schur D‐stability range of an interval matrix presented.

Matrix eigenvalues theory and matrix measure approach.

Several simple sufficient conditions (criteria) for guaranteeing the Schur D‐stability of interval matrices are derived, two equivalence relations between the Schur D‐stability and the vertex stability of interval matrices are proposed, and a new Schur D‐stability range of an interval matrix is presented.

Control theory or stability theory. These stability criterion possess simple forms and provide useful tools to check Schur D‐stability of interval matrices (including point matrix) at first stage.

The paper provides useful tools to check Schur D‐stability of interval matrices (including point matrix) at first stage.

Two equivalence relations between the Schur D‐stability and the vertex stability for general interval matrices (including point matrix) are proposed, such that the conditional limitations for tridiagonal matrix in recent papers are broken. A new Schur D‐stability range of an interval matrix is presented, and several simple sufficient conditions are obtained which guarantee the Schur D‐stability of interval matrices (including point matrix).

The DC‐DC converters which convert one level of electrical voltage to the desired level are widely used in many electrical peripherals. During the past two decade, many different control laws have been developed. The proportional‐integral (PI) control and sliding‐mode control have been carried out for the DC‐DC converters since they are simple to implement and easy to design. However, its performance using PI control and sliding‐mode control is obviously quite limited. The purpose of this paper is to a self‐tuning nonlinear function control (STNFC) propose for the DC‐DC converters. The adaptation laws of the proposed STNFC system are derived in the sense of Lyapunov function, thus not only the controller parameters can be online tuned itself, but also the system's stability can be guaranteed.

In general, the accurate mathematical models of the DC‐DC converters are difficult to derive. This paper proposes a model‐free STNFC design method. Since the proposed STNFC uses a simple fuzzy system with three fuzzy rules base to implement the control law, the computational loading of the fuzzy inference mechanism is slight. So the proposed STNFC system is suitable for the real‐time practical applications. The controller parameters of the proposed STNFC system can online tune in the Lyapunov sense, thus the stability of closed‐loop system can be guaranteed.

The proposed STNFC system is applied to a DC‐DC converter based on a field‐programmable gate array chip. The experimental results are provided to demonstrate the proposed STNFC system can cope with the input voltage and load resistance variations to ensure the stability while providing fast transient response.

The proposed STNFC approach is interesting for the design of an intelligent control scheme. The main contributions of this paper are: the successful development of STNFC system without heavy computational loading. The parameter‐learning algorithm is design based on the Lyapunov stability theorem to guarantee the system stability; the successful applications of the STNFC system to control the forward DC‐DC converter. And, the proposed STNFC methodology can be easily extended to other DC‐DC converters.

The purpose of this paper is to examine the attitude control problem of a certain and big flexible satellite with unmodeled dynamics and unknown bounded disturbances and control input saturation; and to present a design method of robust adaptive controllers (RACs).

First, using the Lyapunov stability theory, it is shown that the proposed adaptive controller can guarantee the stability of the nonlinear system. Then, the parameters regulation method of the RAC is introduced. Finally, an RAC is designed for the object satellite model consisted of all the error‐source models.

The simulation results are compared with other results that are derived by using the typical PID controller. It is proved that the designed RAC has some properties of quickly response, high steady‐state precision and strong robustness.

The paper is of value in presenting a design method of RACs aiming at the object satellite with uncertainties and control input saturation.

The purpose of this paper is to present the methodology to the robust stability analysis of a vision‐based control loop in an uncalibrated environment. The type of uncertainties considered is the parametric uncertainties. The approach adopted in this paper utilizes quadratic Lyapunov function to determine the composite Jacobian matrix and ensures the robust stability using linear matrix inequality (LMI) optimization. The effectiveness of the proposed approach can be witnessed by applying it to two‐link robotic manipulator with the camera mounted on the end‐effector.

The objective of this research is the analysis of uncertain nonlinear system by representing it in differential‐algebraic form. By invoking the suitable system representation and Lyapunov analysis, the stability conditions are described in terms of linear matrix inequalities.

The proposed method is proved robust in the presence of parametric uncertainties.

Through a differential‐algebraic equation, LMI conditions are devised that ensure the stability of the uncertain system while providing an estimate of the domain of attraction based upon quadratic Lyapunov function.

The purpose of this paper is to present an adaptive neuro‐sliding mode control scheme for uncertain nonlinear systems with Lyapunov approach.

The paper focuses on neural network (NN) adaptive control for nonlinear systems in the presence of parametric uncertainties. The plant model structure is represented by a NNs system. The essential idea of the online parametric estimation of the plant model is based on a comparison of the measured state with the estimated one. The proposed adaptive neural controller takes advantages of both the sliding mode control and proportional integral (PI) control. The chattering phenomenon is attenuated and robust performances are ensured. Based on Lyapunov stability theorem, the proposed adaptive neural control system can guarantee the stability of the whole closed‐loop system and obtain good‐tracking performances. Adaptive laws are proposed to adjust the free parameters of the neural models.

Simulation results show that the adaptive neuro‐sliding mode control approach works satisfactorily for nonlinear systems in the presence of parametric uncertainties.

The proposed adaptive neuro‐sliding mode control approach is a mixture of classical neural controller with a supervisory controller. The PI controller is used to attenuate the chattering phenomena. Based on the Lyapunov stability theorem, it is rigorously proved that the stability of the whole closed‐loop system is ensured and the tracking performance is achieved.

The purpose of this paper is to present a nonlinear model along with stability analysis of a flexible supersonic flight vehicle system.

The mathematical state space nonlinear model of the system is derived using Lagrangian approach such that the applied force, moment, and generalized force are all assumed to be nonlinear functions of the system states. The condition under which the system would be unstable is derived and when the system is stable, the region of attraction of the system equilibrium state is determined using the Lyapunov theory and sum of squares optimization method. The method is applied to a slender flexible body vehicle, which is referenced by the other researchers in the literature.

It is demonstrated that neglecting the nonlinearity in external force, moment and generalized force, as it was assumed by other researchers, can cause significant variations in stability conditions. Moreover, when the system is stable, it is shown analytically here that a reduction in dynamic pressure can make a larger region of attraction, and thus instability will occur in a larger angle of attack, greater angular velocity and elastic displacement.

In order to carefully study the behavior of aeroelastic flight vehicle, a nonlinear model and analysis is definitely necessary. Moreover, for the design of the airframe and/or control purposes, it is essential to investigate region of attraction of equilibrium state of the stable flight vehicle.

Current stability analysis methods for nonlinear elastic flight vehicles are unable to determine the state space region where the system is stable. Nonlinear modeling affects the determination of the stability region and instability condition. This paper presents a new approach to stability analysis of the nonlinear flexible flight vehicle. By determining the region of attraction when the system is stable, it is demonstrated analytically, in this research, that decreasing the dynamic pressure can produce larger region of attraction.