Robust Stability/Performance Analysis for Linear Time-Invariant Polynomially Parameter-Dependent Systems using Polynomially Parameter-Dependent Lyapunov Functions

2006 ◽  
Author(s):  
Masayuki Sato ◽  
Dimitri Peaucelle
Keyword(s):  
Performance Analysis ◽  
Robust Stability ◽  
Lyapunov Functions ◽  
Linear Time ◽  
Linear Time Invariant ◽  
Stability Performance ◽  
Parameter Dependent ◽  
Time Invariant

Reduction in the Number of Gain-Scheduling Parameters Using Dimensional Transformation

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Haftay Hailu ◽  
Sean Brennan
Keyword(s):  
Linear Time ◽  
Gain Scheduling ◽  
Linear Parameter Varying ◽  
Linear Time Invariant ◽  
Lti System ◽  
Gain Scheduled Controller ◽  
Parameter Dependent ◽  
Time Invariant ◽  
Linear Parameter Varying System ◽  
Gain Scheduled

A method is presented that can often reduce the number of scheduling parameters for gain-scheduled controller implementation by transformation of the system representation using parameter-dependent dimensional transformations. In some cases, the reduction in parameter dependence is so significant that a linear parameter-varying system can be transformed to an equivalent linear time invariant (LTI) system, and a simple example of this is given. A general analysis of the parameter-dependent dimensional transformation using a matrix-based approach is then presented. It is shown that, while some transformations simplify gain scheduling, others may increase the number of scheduling parameters. This work explores the mathematical conditions causing an increase or decrease in varying parameters resulting from a given transformation, thereby allowing one to seek transformations that most reduce the number of gain-scheduled parameters in the controller synthesis step.

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