Stability and performance for a class of discrete-time Markovian jump non-linear systems

• Grant number: 12/17188-0
• Support type: Scholarships in Brazil - Post-Doctorate
• Effective date (Start): December 01, 2012
• Effective date (End): June 30, 2013
• Field of knowledge: Engineering - Electrical Engineering - Industrial Electronics, Electronic Systems and Controls
• Principal Investigator: Oswaldo Luiz Do Valle Costa
• Grantee: Carlos Alberto Cavichioli Gonzaga
• Home Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

In this project, to be developed by the grantee Dr. Carlos A. C. Gonzaga in cooperation with Prof. Oswaldo Luiz do Valle Costa, the class of discrete-time markovian jump Lur'e systems will be addressed. Thus, these systems will exhibit mode-dependent cone bounded non-linearities, and the switching behaviour depends on the Markov chain variable. Stability and performance analysis problems will be studied, as well as the control synthesis with input saturation. By making use of stochastic Lyapunov functions, the research will not only consider the classical quadratic in the state function. We will extend the new Lur'e-type Lyapunov function, proposed in the Ph.D work of the grantee. Such a function covers straightforwardly the case of switching markovian non-linearities and is able to establish stability conditions only by requiring the sector condition, relaxing the classical bounded variation assumptions. With respect to the local stability analysis, the level set of our function, which may be non-convex and disconnected, will be employed to provide an estimate of the basin of attraction since it is suitable to the non-linear nature of these systems.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

CAVICHIOLI GONZAGA, CARLOS ALBERTO; COSTA, OSWALDO LUIZ V. Stochastic stabilization and induced l(2)-gain for discrete-time Markov jump Lur'e systems with control saturation. AUTOMATICA, v. 50, n. 9, p. 2397-2404, SEP 2014. Web of Science Citations: 14.

COSTA, O. L. V.; GONZAGA, C. A. C. Quadratic and H-infinity switching control for discrete-time linear systems with multiplicative noises. International Journal of Control, v. 87, n. 11, p. 2312-2326, 2014. Web of Science Citations: 2.