Robust Stability of Sequential Multi-input Multi-output Quantitative Feedback Theory Designs

2004 ◽  
Vol 127 (2) ◽  
pp. 250-256 ◽  
Author(s):  
Murray L. Kerr ◽  
Suhada Jayasuriya ◽  
Samuel F. Asokanthan
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Internal Stability ◽  
Quantitative Feedback Theory ◽  
Recursive Design ◽  
Stability Theorems ◽  
Improved Design ◽  
The Stability ◽  
Necessary And Sufficient

This paper re-examines the stability of multi-input multi-output (MIMO) control systems designed using sequential MIMO quantitative feedback theory (QFT). In order to establish the results, recursive design equations for the SISO equivalent plants employed in a sequential MIMO QFT design are established. The equations apply to sequential MIMO QFT designs in both the direct plant domain, which employs the elements of plant in the design, and the inverse plant domain, which employs the elements of the plant inverse in the design. Stability theorems that employ necessary and sufficient conditions for robust closed-loop internal stability are developed for sequential MIMO QFT designs in both domains. The theorems and design equations facilitate less conservative designs and improved design transparency.

scholarly journals Lyapunov Characterization for the Stability of Stochastic Control Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fakhreddin Abedi ◽  
Wah June Leong ◽  
Mohammad Abedi
Keyword(s):  
Control Systems ◽  
Stochastic Control ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Stability ◽  
Necessary And Sufficient

Lyapunov-like characterization for the problem of input-to-state stability in the probability of nonautonomous stochastic control systems is established. We extend the well-known Artstein-Sontag theorem to derive the necessary and sufficient conditions for the input-to-state stabilization of stochastic control systems. Illustrating example is provided.

On the Necessary and Sufficient Conditions for the Stability of Linear Generalized Ordinary Differential, Linear Impulsive and Linear Difference Systems

2009 ◽  
Vol 16 (4) ◽  
pp. 597-616
Author(s):  
Shota Akhalaia ◽  
Malkhaz Ashordia ◽  
Nestan Kekelia
Keyword(s):  
Linear System ◽  
Difference Equations ◽  
Closed Interval ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Difference Systems ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Generalized Ordinary Differential Equations ◽  
Lyapunov Sense

Abstract Necessary and sufficient conditions are established for the stability in the Lyapunov sense of solutions of a linear system of generalized ordinary differential equations 𝑑𝑥(𝑡) = 𝑑𝐴(𝑡) · 𝑥(𝑡) + 𝑑𝑓(𝑡), where and are, respectively, matrix- and vector-functions with bounded total variation components on every closed interval from . The results are realized for the linear systems of impulsive, ordinary differential and difference equations.

Quasi-Periodic Motion and Hopf Bifurcation of a Two-Dimensional Aeroelastic Airfoil System in Supersonic Flow

2021 ◽  
Vol 31 (02) ◽  
pp. 2150018
Author(s):  
Wentao Huang ◽  
Chengcheng Cao ◽  
Dongping He
Keyword(s):  
Hopf Bifurcation ◽  
Sufficient Conditions ◽  
Theoretical Method ◽  
Simulation Method ◽  
Runge Kutta Method ◽  
Complex Roots ◽  
The Stability ◽  
Necessary And Sufficient ◽  
2D And 3D ◽  
Imaginary Roots

In this article, the complex dynamic behavior of a nonlinear aeroelastic airfoil model with cubic nonlinear pitching stiffness is investigated by applying a theoretical method and numerical simulation method. First, through calculating the Jacobian of the nonlinear system at equilibrium, we obtain necessary and sufficient conditions when this system has two classes of degenerated equilibria. They are described as: (1) one pair of purely imaginary roots and one pair of conjugate complex roots with negative real parts; (2) two pairs of purely imaginary roots under nonresonant conditions. Then, with the aid of center manifold and normal form theories, we not only derive the stability conditions of the initial and nonzero equilibria, but also get the explicit expressions of the critical bifurcation lines resulting in static bifurcation and Hopf bifurcation. Specifically, quasi-periodic motions on 2D and 3D tori are found in the neighborhoods of the initial and nonzero equilibria under certain parameter conditions. Finally, the numerical simulations performed by the fourth-order Runge–Kutta method provide a good agreement with the results of theoretical analysis.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

scholarly journals Multiresolution analysis and wavelets on Vilenkin groups

2008 ◽  
Vol 21 (3) ◽  
pp. 309-325 ◽  
Author(s):  
Yury Farkov
Keyword(s):  
Multiresolution Analysis ◽  
Linear Independence ◽  
Sufficient Conditions ◽  
Partition Of Unity ◽  
Necessary And Sufficient Conditions ◽  
Refinable Functions ◽  
Vilenkin Groups ◽  
Orthogonal Wavelets ◽  
The Stability ◽  
Necessary And Sufficient

This paper gives a review of multiresolution analysis and compactly sup- ported orthogonal wavelets on Vilenkin groups. The Strang-Fix condition, the partition of unity property, the linear independence, the stability, and the orthonormality of 'integer shifts' of the corresponding refinable functions are considered. Necessary and sufficient conditions are given for refinable functions to generate a multiresolution analysis in the L2-spaces on Vilenkin groups. Several examples are provided to illustrate these results. .

Dynamical Behaviors of a Fractional-Order Predator–Prey Model with Holling Type IV Functional Response and Its Discretization

2019 ◽  
Vol 20 (2) ◽  
pp. 125-136
Author(s):  
A. M. Yousef ◽  
S. Z. Rida ◽  
Y. Gh. Gouda ◽  
A. S. Zaki
Keyword(s):  
Functional Response ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Dynamical Behaviors ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Theoretical Results

AbstractIn this paper, we investigate the dynamical behaviors of a fractional-order predator–prey with Holling type IV functional response and its discretized counterpart. First, we seek the local stability of equilibria for the fractional-order model. Also, the necessary and sufficient conditions of the stability of the discretized model are achieved. Bifurcation types (include transcritical, flip and Neimark–Sacker) and chaos are discussed in the discretized system. Finally, numerical simulations are executed to assure the validity of the obtained theoretical results.

Finite-time dissipative control for networked control systems with hybrid-triggered scheme

2020 ◽  
pp. 014233122094650
Author(s):  
Qian Zhang ◽  
Huaicheng Yan ◽  
Shiming Chen ◽  
Xisheng Zhan ◽  
Xiaowei Jiang
Keyword(s):  
Control Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Closed Loop System ◽  
Network Resources ◽  
Dissipative Control

This paper is concerned with the problem of finite-time dissipative control for networked control systems by hybrid triggered scheme. In order to save network resources, a hybrid triggered scheme is proposed, which consists of time-triggered scheme and event-triggered scheme simultaneously. Firstly, sufficient conditions are derived to guarantee that the closed-loop system is finite-time bounded (FTBD) and [Formula: see text] dissipative. Secondly, the corresponding controller design approach is presented based on the derived conditions. Finally, a numerical example is presented to show the effectiveness of the proposed approach.

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