An almost necessary and sufficient condition for robust stability of closed-loop systems with disturbance observer

Automatica ◽  
2009 ◽  
Vol 45 (1) ◽  
pp. 296-299 ◽  
Author(s):  
Hyungbo Shim ◽  
Nam H. Jo
Keyword(s):  
Robust Stability ◽  
Disturbance Observer ◽  
Closed Loop ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Loop Systems ◽  
Necessary And Sufficient

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.

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.

A New Algorithm for Testing the Stability of a Polytope: A Geometric Approach for Simplification

1996 ◽  
Vol 118 (3) ◽  
pp. 611-615 ◽  
Author(s):  
Jinsiang Shaw ◽  
Suhada Jayasuriya
Keyword(s):  
Characteristic Equation ◽  
Robust Stability ◽  
Geometric Structure ◽  
Geometric Approach ◽  
Geometric Interpretation ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Edge Theorem

Considered in this paper is the robust stability of a class of systems in which a relevant characteristic equation is a family of polynomials F: f(s, q) = a0(q) + a1(q)s + … + an(q)sn with its coefficients ai(q) depending linearly on q unknown-but-bounded parameters, q = (p1, p2, …, pq)T. It is known that a necessary and sufficient condition for determining the stability of such a family of polynomials is that polynomials at all the exposed edges of the polytope of F in the coefficient space be stable (the edge theorem of Bartlett et al., 1988). The geometric structure of such a family of polynomials is investigated and an approach is given, by which the number of edges of the polytope that need to be checked for stability can be reduced considerably. An example is included to illustrate the benefit of this geometric interpretation.

ROBUST STABILITY OF MULTI-DIMENSIONAL (m-D) DISCRETE INTERVAL SYSTEMS AND APPLICATIONS

1991 ◽  
Vol 01 (01) ◽  
pp. 93-104 ◽  
Author(s):  
P. BAUER
Keyword(s):  
Robust Stability ◽  
Discrete Systems ◽  
Sufficient Condition ◽  
Invariant System ◽  
Necessary And Sufficient Condition ◽  
Interval System ◽  
Discrete Interval ◽  
The Stability ◽  
Necessary And Sufficient ◽  
Interval Systems

Robust stability of m-D discrete systems, represented by a m-D difference equation is analyzed. A sufficient condition for stability is derived, which requires the stability of one linear shift-invariant system. For special classes of systems, the stability of one corner of the interval system is a necessary and sufficient condition. The results are applicable to shift-variant and shift-invariant interval m-D systems. Applications and illustrative examples are also provided.

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