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.
News published in Agência FAPESP Newsletter about the scholarship: