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Discrete-time H∞ control problem for nonlinear descriptor systems
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DOI：10.1109/TAC.2008.919543.png)
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Abstract
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This note presents an explicit solution to the problem of disturbance attenuation with internal stability for discrete-time nonlinear descriptor systems. Both the static-state feedback and dynamic output feedback cases are considered. In particular, we characterize a family of H-infinity controllers solving the problem locally around a neighborhood of the origin. To do this, we first derive two stability criteria for discrete-time nonlinear descriptor systems, and then, a version of a bounded real lemma is also developed based on the concepts of dissipation inequality and differential game. After that, the results are used to derive the H-infinity control theory for nonlinear discrete-time descriptor systems. The approach taken is mainly algebraic, and hence is simple and clear.
Keywords:
bounded real lemma
descriptor systems
discrete-time systems
Hamilton-Jacobi inequality
nonlinear H-infinity control
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