Necessary and sufficient condition for robust stability of linear distributed feedback systems†

1982 ◽  
Vol 35 (2) ◽  
pp. 255-267 ◽  
Author(s):  
M. J. CHEN ◽  
C. A. DESOER
Keyword(s):  
Robust Stability ◽  
Distributed Feedback ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Feedback Systems ◽  
Necessary And Sufficient

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.

Sign in / Sign up

Export Citation Format

Share Document