Exponential Stability Region Estimates for the State-Dependent Riccati Equation Controllers

Abstract

We investigate the nonlinear exponential stability of the State-Dependent Riccati Equation (SDRE)-based control. The SDRE technique is a nonlinear control method, which has emerged since the mid 1990's and has been applied to a wide range of nonlinear control problems. Despite the systematic method of SDRE, it is difficult to prove stability because the general analytic solution to the SDRE is not known. Some notable prior work has shown local asymptotic stability of SDRE by using numerical and analytical methods. In this paper, we introduce a new strategy, based on contraction analysis, to estimate the exponential stability region for SDRE controlled systems. Examples demonstrate the superiority of the proposed method.

Additional Information

© 2009 IEEE. Date of Conference: 15-18 Dec. 2009. Date Added to IEEE Xplore: 29 January 2010. This work was supported by the Air Force Office of Scientific Research (AFOSR). The authors thank Prof. J. Oliver at the Virtual Reality Application Center, Iowa State University for his support. The authors gratefully acknowledge stimulating discussions with Prof. J.-J. E. Slotine, Dr. W. Lohmiller, and A. A. Paranjape.

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