Robust kalman filter design for markovian jump linear systems with norm-bounded unknown nonlinearities

• Published in: Circuits, systems, and signal processing systems, and signal processing, 2005-04, Vol.24 (2), p.135-150
• Main Authors: PENG SHI, KARAN, Mehmet, KAYA, C. Yalcin
• Format: Article
• Language: English
• Subjects: Applied sciences; Control theory; Detection, estimation, filtering, equalization, prediction; Error analysis; Exact sciences and technology; Filter design (mathematics); Hybrid systems; Information, signal and communications theory; Kalman filters; Linear systems; Markov analysis; Markov processes; Nonlinear systems; Nonlinearity; Parameters; Riccati equation; Robustness; Signal and communications theory; Signal, noise; State vectors; Telecommunications and information theory; Uncertainty; Upper bounds
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-004-0702-2

This paper considers the problems of stability and filtering for a class of linear hybrid systems with nonlinear uncertainties and Markovian jump parameters. The hybrid system under study involves a continuous-valued system state vector and a discretevalued system mode. The unknown nonlinearities in the system are time varying and norm bounded. The Markovian jump parameters are modeled by a Markov process with a finite number of states. First, we show the equivalence of the sets of norm-bounded linear and nonlinear uncertainties. Then, instead of the original hybrid linear system with nonlinear uncertainties, we consider the same system with linear uncertainties. By using a Riccati equation approach for this new system, a robust filter is designed using two sets of coupled Riccati-like equations such that the estimation error is guaranteed to have an upper bound.[PUBLICATION ABSTRACT]