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A Delay-Dependent Approach to Robust Filtering for LPV Systems with Discrete and Distributed Delays using PPDQ Functions

Hamid Reza Karimi, Boris Lohmann, and Christof Büskens
International Journal of Control, Automation, and Systems, vol. 5, no. 2, pp.170-183, 2007

Abstract : This paper presents a delay-dependent approach to robust filtering for linear parameter-varying (LPV) systems with discrete and distributed time-invariant delays in the states and outputs. It is assumed that the state-space matrices affinely depend on parameters that are measurable in real-time. Some new parameter-dependent delay-dependent stability conditions are established in terms of linear matrix inequalities (LMIs) such that the filtering process remains asymptotically stable and satisfies a prescribed H∞ performance level. Using polynomially parameter-dependent quadratic (PPDQ) functions and some Lagrange multiplier matrices, we establish the parameter-independent delay-dependent conditions with high precision under which the desired robust H∞ filters exist and derive the explicit expression of these filters. A numerical example is provided to demonstrate the validity of the proposed design approach.

Keyword : Delay, LPV systems, H∞ filtering, LMI, polynomially parameter-dependent quadratic functions.

 
 
 
 
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