scholarly journals Disturbance Decoupling Problem: Logic-Dynamic Approach-Based Solution

Symmetry ◽  
2019 ◽  
Vol 11 (4) ◽  
pp. 555 ◽  
Author(s):  
Alexey Zhirabok
Keyword(s):  
Control Systems ◽  
Sufficient Conditions ◽  
Algebraic Approach ◽  
Dynamic Measurement ◽  
Dynamic Approach ◽  
Smooth Functions ◽  
System Description ◽  
Disturbance Decoupling ◽  
Measurement Feedback ◽  
Necessary And Sufficient

This paper considers the disturbance decoupling problem by the dynamic measurement feedback for discrete-time nonlinear control systems. To solve this problem, the algebraic approach, called the logic-dynamic approach, is used. Such an approach assumes that the system description may contain non-smooth functions. Necessary and sufficient conditions are obtained in terms of matrices similar to controlled and ( h , f ) -invariant functions. Furthermore, procedures are developed to determine the corresponding matrices and the dynamic measurement feedback.

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.

Observer-based control for a singular Markovian jumping system

2017 ◽  
Vol 34 (1) ◽  
pp. 33-52
Author(s):  
Ching-Min Lee
Keyword(s):  
Control Problem ◽  
Control Systems ◽  
Discrete Time ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Markovian Jumping ◽  
Content Type ◽  
Robot Systems ◽  
Necessary And Sufficient

Purpose For most practical control system problems, the state variables of a system are not often available or measureable due to technical or economical constraints. In these cases, an observer-based controller design problem, which is involved with using the available information on inputs and outputs to reconstruct the unmeasured states, is desirable, and it has been wide investigated in many practical applications. However, the investigation on a discrete-time singular Markovian jumping system is few so far. This paper aims to consider an observer-based control problem for a discrete-time singular Markovian jumping system and provides a set of easy-used conditions to the proposed control law. Design/methodology/approach According to the connotation of the separation principle extended from linear systems, a mode-dependent observer and a state-feedback controller is designed and carried out independently via two sets of derived necessary and sufficient conditions in terms of linear matrix inequalities (LMIs). Findings A set of necessary and sufficient conditions for an admissibility analysis problem related to a discrete-time singular Markovian jumping system is derived to be a doctrinal foundation for the proposed design problems. A mode-dependent observer and a controller for such systems could be designed via two sets of strictly LMI-based synthesis conditions. Research limitations/implications The proposed method can be applied to discrete-time singular Markovian jumping systems with transition probability pij > 0 rather than the ones with pii = 0. Practical implications The formulated problem and proposed methods have extensive applications in various fields such as power systems, electrical circuits, robot systems, chemical systems, networked control systems and interconnected large-scale systems. Take robotic networked control systems for example. It is recognized that the variance phenomena derived from network transmission, such as packets dropout, loss and disorder, are suitable for modeling as a system with Markovian jumping modes, while the dynamics of the robot systems can be described by singular systems. In addition, the packets dropout or loss might result in unreliable transmission signals which motivates an observer-based control problem. Originality/value Both of the resultant conditions of analysis and synthesis problems for a discrete-time singular Markovian jumping system are necessary and sufficient, and are formed in strict LMIs, which can be used and implemented easily via MATLAB toolbox.

scholarly journals The classical theory of calculus of variations for generalized functions

2017 ◽  
Vol 8 (1) ◽  
pp. 779-808 ◽  
Author(s):  
Alexander Lecke ◽  
Lorenzo Luperi Baglini ◽  
Paolo Giordano
Keyword(s):  
Calculus Of Variations ◽  
Classical Theory ◽  
Sufficient Conditions ◽  
Generalized Functions ◽  
Conjugate Points ◽  
Lagrange Equations ◽  
Smooth Functions ◽  
Nonlinear Properties ◽  
Schwartz Distributions ◽  
Necessary And Sufficient

Abstract We present an extension of the classical theory of calculus of variations to generalized functions. The framework is the category of generalized smooth functions, which includes Schwartz distributions, while sharing many nonlinear properties with ordinary smooth functions. We prove full connections between extremals and Euler–Lagrange equations, classical necessary and sufficient conditions to have a minimizer, the necessary Legendre condition, Jacobi’s theorem on conjugate points and Noether’s theorem. We close with an application to low regularity Riemannian geometry.

scholarly journals Automatic choice of parameters at approximation of functions by rational splines

1987 ◽  
pp. 52
Author(s):  
A.D. Malysheva
Keyword(s):  
Sufficient Conditions ◽  
Order Of Approximation ◽  
Approximation Of Functions ◽  
Smooth Functions ◽  
Higher Derivatives ◽  
Necessary And Sufficient ◽  
Automatic Choice ◽  
Derivatives Of ◽  
Best Parameters ◽  
Approximation Of A Function

We obtain necessary and sufficient conditions put on the parameters of rational splines that provide given order of approximation of smooth functions. We point out the formulas of asymptotically the best parameters of rational splines that, while providing the best order of approximation of a function by rational splines, do not contain information about the values of higher derivatives of a function.

Delay-independent Stability of Uncertain Control Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 277-283 ◽  
Author(s):  
Ilhan Tuzcu ◽  
Mehdi Ahmadian
Keyword(s):  
Control Systems ◽  
Uncertain Systems ◽  
Extreme Values ◽  
Sufficient Conditions ◽  
Entire Family ◽  
Active Vibration ◽  
Delay Differential Systems ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Analytical Expressions

This paper will provide a study of the delay-independent stability of uncertain control systems, represented by a family of quasipolynomials with single time-delays. The uncertain systems that are considered here are delay differential systems whose parameters are known only by their lower and upper bounds. The results are given in the form of necessary and sufficient conditions along with the assumptions for the quasipolynomial families considered. The conditions are transformed into convenient forms, which provide analytical expressions that can be easily checked by commercially available computing tools. For uncertain systems represented by families of quasipolynomials, it is shown that the delay independent stability for the extreme values of parameters is not sufficient for the delay independent stability of the entire family. In addition, the family must satisfy some conditions for the interior values of each parameter within specially constructed frequency ranges. The implementation of the theorem that is suggested is demonstrated on an example system that includes a single degree of freedom system with an active vibration absorber, namely the Delayed Resonator.

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