Abstract
This paper presents the development of a new model reduction method for discrete-time bilinear systems based on the balanced truncation framework. In many model reduction applications, it is advantageous to analyze the characteristics of the system with emphasis on particular frequency intervals of interest. In order to analyze the degree of controllability and observability of discrete-time bilinear systems with emphasis on particular frequency intervals of interest, new generalized frequency interval controllability and observability gramians are introduced in this paper. These gramians are the solution to a pair of new generalized Lyapunov equations. The conditions for solvability of these new generalized Lyapunov equations are derived and a numerical solution method for solving these generalized Lyapunov equations is presented. Numerical examples which illustrate the usage of the new generalized frequency interval controllability and observability gramians as part of the balanced truncation framework ...
Highlights
Model reduction which is of fundamental importance in many modeling and control applications deals with the approximation of a higher order model by a lower order model such that the input–output behavior of the original system is preserved to a required accuracy
To address the complexity associated with highorder models, we present a new model reduction technique for discrete-time bilinear systems
One of the further developments to the original balanced truncation technique was the work by Gawronski and Juang which involved the development of frequency interval controllability and observability gramians (Gawronski & Juang, 1990)
Summary
Model reduction which is of fundamental importance in many modeling and control applications deals with the approximation of a higher order model by a lower order model such that the input–output behavior of the original system is preserved to a required accuracy. The balanced truncation model reduction technique originally developed by Moore for continuous-time linear systems is one of the most widely applied model reduction techniques (Moore, 1981). One of the further developments to the original balanced truncation technique was the work by Gawronski and Juang which involved the development of frequency interval controllability and observability gramians (Gawronski & Juang, 1990). In the context of discrete-time systems, digital systems are designed to work with signals with known frequency characteristics, it is essential to have model reduction techniques which generate reduced-order models which function well with signals which have specified frequency characteristics. The works by Horta, Juang, and Longman (1993), Wang and Zilouchian (2000) and more recently by Imran and Ghafoor (2014) described the formulation of frequency interval gramians for discrete-time systems
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