scholarly journals Positive Stabilization of Linear Differential Algebraic Equation System

2016 ◽  
Vol 2016 ◽  
pp. 1-3 ◽  
Author(s):  
Muhafzan
Keyword(s):  
Algebraic Equation ◽  
State Feedback ◽  
Closed Loop ◽  
Equation System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Loop System ◽  
Differential Algebraic Equation ◽  
Linear Differential ◽  
Necessary And Sufficient

We study in this paper the existence of a feedback for linear differential algebraic equation system such that the closed-loop system is positive and stable. A necessary and sufficient condition for such existence has been established. This result can be used to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.

On Stability in Nonsequential MIMO QFT Designs

2004 ◽  
Vol 127 (1) ◽  
pp. 98-104 ◽  
Author(s):  
Murray L. Kerr ◽  
Suhada Jayasuriya ◽  
Samuel F. Asokanthan
Keyword(s):  
Design Methodology ◽  
Closed Loop ◽  
Stability Theorem ◽  
Loop System ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Loop System ◽  
Closed Loop Systems ◽  
The Stability ◽  
Necessary And Sufficient

This paper reexamines the stability of uncertain closed-loop systems resulting from the nonsequential (NS) MIMO QFT design methodology. By combining the effect of satisfying both the robust stability and robust performance specifications in a NS MIMO QFT design, a proof for the stability of the uncertain closed-loop system is derived. The stability theorem proves that, subject to the satisfaction of a critical necessary and sufficient condition, the original NS MIMO QFT design methodology will provide a robustly stable closed-loop system. This necessary and sufficient condition provides a useful existence test for a successful NS MIMO QFT design. The results expose the salient features of the NS MIMO QFT design methodology. Two 2×2 MIMO design examples are presented to illustrate the key features of the stability theorem.

The uniform exponential stability of a class of linear differential–difference equations in a Hilbert space

1981 ◽  
Vol 89 (3-4) ◽  
pp. 201-215 ◽  
Author(s):  
Richard Datko
Keyword(s):  
Hilbert Space ◽  
Phase Space ◽  
Exponential Stability ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Exponential Stability ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is given for the uniform exponential stability of certain autonomous differential–difference equations whose phase space is a Hilbert space. It is shown that this property is preserved when the delays depend homogeneously on a nonnegative parameter.

5.—The Uniform Asymptotic Stability of Certain Linear Differential-difference Equations

1976 ◽  
Vol 74 ◽  
pp. 71-79
Author(s):  
R. Datko
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Difference Equations ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Uniform Asymptotic Stability ◽  
Linear Ordinary Differential Equations ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition is developed for determination of the uniform stability of a class of non-autonomous linear differential-difference equations. This condition is the analogue of the Liapunov criterion for linear ordinary differential equations.

scholarly journals Plug and Play Robust Distributed Control with Ellipsoidal Parametric Uncertainty System

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Hong Wang-jian ◽  
Wang Yan-xiang
Keyword(s):  
Linear System ◽  
Distributed Control ◽  
Control Strategy ◽  
State Feedback ◽  
Parametric Uncertainty ◽  
State Feedback Control ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Plug And Play ◽  
Necessary And Sufficient

We consider a continuous linear time invariant system with ellipsoidal parametric uncertainty structured into subsystems. Since the design of a local controller uses only information on a subsystem and its neighbours, we combine the plug and play idea and robust distributed control to propose one distributed control strategy for linear system with ellipsoidal parametric uncertainty. Firstly for linear system with ellipsoidal parametric uncertainty, a necessary and sufficient condition for robust state feedback control is proposed by means of linear matrix inequality. If this necessary and sufficient condition is satisfied, this robust state feedback gain matrix can be easily derived to guarantee robust stability and prescribed closed loop performance. Secondly the plug and play idea is introduced in the design process. Finally by one example of aircraft flutter model parameter identification, the efficiency of the proposed control strategy can be easily realized.

Characterisation of the factors of quasi-differential expressions

1992 ◽  
Vol 120 (3-4) ◽  
pp. 297-312
Author(s):  
D. Race ◽  
A. Zettl
Keyword(s):  
Differential Expression ◽  
Null Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
General Scalar ◽  
Linear Differential ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition for a general, scalar, quasi-differential expression of order n to be factorisable into a product of expressions of order n − k and k, for any 0 < k < n, is given. The factors are characterised completely in terms of elements of the null space of the expression and its adjoint. The results obtained extend existing results due to both Polya and Zettl from the case of classical linear differential expressions to quasi-differential expressions.

Exponentially Dissipative Control for Singular Impulsive Dynamical Systems

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Li Yang ◽  
Xinzhi Liu ◽  
Zhigang Zhang
Keyword(s):  
Dynamical Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Dissipative Control ◽  
Necessary And Sufficient

This paper studies the problem of exponentially dissipative control for singular impulsive dynamical systems. Some necessary and sufficient conditions for exponential dissipativity of such systems are established in terms of linear matrix inequalities (LMIs). A state feedback controller is designed to make the closed-loop system exponentially dissipative. A numerical example is given to illustrate the feasibility of the method.

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