DocumentCode :
3159831
Title :
Mean Square Stability Analysis of Hybrid Jump Linear Systems using a Markov Kernel Approach
Author :
Tejada, Arturo ; Herencia-Zapana, Heber ; González, Oscar R. ; Gray, W. Steven
Author_Institution :
Old Dominion Univ., Norfolk
fYear :
2007
fDate :
9-13 July 2007
Firstpage :
3482
Lastpage :
3487
Abstract :
Hybrid jump linear systems (HJLS´s) were recently introduced to study the fundamental properties of supervisory control systems. In this paper, their mean square (MS) stability is analyzed through a modified lifting technique adapted from the literature on Markov jump linear systems. The original technique tests whether rho(A), the spectral radius of a second moment transition matrix A (which contains the transition probabilities of the Markov chain driving the jump linear system), is less than 1. Here, the test is adapted to yield two new sufficient MS stability conditions. The first condition applies to jump linear systems driven by general finite-state stochastic processes. It requires computing and testing the spectral radius of the matrix AMthetas tilde, which is not a second moment transition matrix, using estimated upper bounds of the transition probabilities associated with the processes driving the system. The second condition applies to a large subclass of HJLS´s and makes use of the Markov kernel associated with HJLS´s to test rho(AMz), a particular instance of rho(AMthetas tilde). These results are illustrated through the stability analysis of an AFTI-F16 aircraft deployed on a computer platform equipped with an advanced error recovery mechanism.
Keywords :
Markov processes; aircraft control; linear systems; matrix algebra; stability; AFTI-F16 aircraft; Markov jump linear systems; Markov kernel approach; advanced error recovery mechanism; finite-state stochastic processes; hybrid jump linear systems; mean square stability analysis; modified lifting technique; second moment; supervisory control systems; Aircraft; Control systems; Kernel; Linear systems; Stability analysis; Stochastic processes; Stochastic systems; Supervisory control; System testing; Upper bound;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
ISSN :
0743-1619
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
Type :
conf
DOI :
10.1109/ACC.2007.4282224
Filename :
4282224
Link To Document :
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