Abstract
This paper investigates the problem of local stabilization of Markov jump nonlinear quadratic systems. A method is presented for the synthesis of a static nonlinear quadratic state feedback control law that ensures the local exponential mean square stability of the zero equilibrium point of the closed-loop system in some polytopic region of the state-space with a guaranteed region of stability inside this polytope. The proposed control design is tailored in terms of linear matrix inequalities together with convex optimization to achieve an enlarged stability region. A numerical example is presented to illustrate the application of the stabilization method.
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