Realization Theory for a Class of Stochastic Bilinear Systems

• Published in: IEEE transactions on automatic control Vol. 63; no. 1; pp. 69 - 84
• Main Authors: Petreczky, Mihaly, Vidal, Rene
• Format: Journal Article
• Language: English
• Published: IEEE 01-01-2018; Institute of Electrical and Electronics Engineers
• Subjects: Automatic; Control systems; Control theory; Electronic mail; Engineering Sciences; Linear systems; Mathematics; Nonlinear systems; Optimization and Control; Random variables; Stochastic processes; Stochastic systems; system identification
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2017.2710801

This paper presents a complete realization theory for a class of discrete-time, bilinear systems with observed stochastic inputs, which we call generalized bilinear systems. This class of systems includes subclasses of bilinear systems, linear parameter varying (LPV) systems, and jump-Markov linear systems. We present necessary and sufficient conditions for the existence of a realization of generalized bilinear systems, along with a characterization of minimality in terms of rank conditions. We also formulate a realization algorithm and a minimization algorithm and we show that minimality can be checked algorithmically.