Some results on finite-time stabilization of Markovian jump nonlinear quadratic systems

The behaviors of a dynamical system over the finite-time interval are often of great importance in many practical situations. In this paper the problem of stabilizing a class of discrete-time Markovian jump nonlinear quadratic systems with partial knowledge on transition probabilities over the finite-time interval is addressed. First, sufficient conditions that warrant the finite-time stochastic boundedness of the system are established. Then, similar conditions that warrant the finite-time stochastic stability of the nonlinear quadratic systems without exogenous disturbance are also derived. Next, design of mode-dependent state feedback controllers that stabilize Markovian jump nonlinear quadratic systems with/without exogenous disturbance is presented. Finally, the obtained theoretical results are evaluated using an illustrative example.