Distance Measures, Robust Stability Conditions and Robust Performance Guarantees for Uncertain Feedback Systems

2006 ◽  
pp. 317-344 ◽  
Author(s):  
George Papageorgiou ◽  
Alexander Lanzon
Keyword(s):  
Robust Stability ◽  
Distance Measures ◽  
Stability Conditions ◽  
Feedback Systems ◽  
Robust Performance ◽  
Performance Guarantees

A New QFT Design Methodology for Feedback Systems Under Input Saturation

1999 ◽  
Vol 123 (2) ◽  
pp. 225-232 ◽  
Author(s):  
Wei Wu ◽  
Suhada Jayasuriya
Keyword(s):  
Robust Stability ◽  
Design Methodology ◽  
Design Method ◽  
Input Saturation ◽  
Function Technique ◽  
Feedback Systems ◽  
Robust Performance ◽  
Saturation Nonlinearity ◽  
Performance Requirements ◽  
And Performance

Presented in this paper is a design methodology for robust stability and robust performance for a large class of plants subject to an input saturation nonlinearity. Based on Horowitz’s 3-DOF linear design method, a more general form for the additional loop transmission around the saturating element is proposed to design the third degree of freedom Hs, for Type n plants, n⩾1. Robust stability is established with the circle criterion and the describing function technique, and robust performance is improved by imposing nonovershooting conditions. All stability and performance requirements are then transferred into frequency domain design bounds which are easily obtained using QFT design techniques. This procedure applies to all SISO, Type n, stable plants with uncertainties (parametric or nonparametric), and to marginally stable and conditionally stable plants as well.

scholarly journals Numerical Computation of Lower Bounds of Structured Singular Values

2018 ◽  
Vol 11 (3) ◽  
pp. 844-868
Author(s):  
M. Fazeel Anwar ◽  
Mutti-Ur Rehman
Keyword(s):  
System Theory ◽  
Linear Algebra ◽  
Lower Bounds ◽  
Robust Stability ◽  
Numerical Approximation ◽  
Singular Values ◽  
Numerical Linear Algebra ◽  
Linear Feedback ◽  
Feedback Systems ◽  
Stability And Instability

In this article we consider the numerical approximation of lower bounds of Structured Singular Values, SSV. The SSV is a wellknown mathematical quantity which is widely used to analyse and syntesize the robust stability and instability analysis of linear feedback systems in control theory. It links a bridge between numerical linear algebra and system theory. The computation of lower bounds of SSV by means of ordinary differential equations based technique is presented. The obtained numerical results for the lower bounds of SSV are compared with the well-known MATLAB function mussv available in MATLAB control toolbox.

In Search of Weaker Conditions to Insure Robust Stability in Linear Feedback Systems

1991 ◽  
Vol 113 (1) ◽  
pp. 168-170
Author(s):  
Yossi Chait ◽  
Nir Cohen ◽  
C. R. MacCluer
Keyword(s):  
Robust Stability ◽  
Approximation Error ◽  
Maximum Modulus ◽  
Linear Feedback ◽  
Sufficient Condition ◽  
Feedback Systems ◽  
Sector Condition ◽  
Plant Uncertainty ◽  
Weaker Conditions

This paper is concerned with the well-known condition for robust stability of systems with plant uncertainty. It is shown that the usual sufficient condition for robust stability, given in terms of the maximum modulus of the plant approximation error, can be relaxed to a sector condition. This sector condition, related to the phase of the uncertain portion of the plant, can increase the range of the allowed variations in the parameters of the uncertain plant sufficient for robust stability.

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