Output Feedback Control of Markovian Jump Repeated Scalar Nonlinear Systems

This paper is concerned with the induced
$\ell _{2}$
dynamic output feedback controller (DOFC) design problem for discrete-time Markovian jump repeated scalar nonlinear systems. By employing both the switching-sequence dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique, a sufficient condition is first established, which guarantees the underlying system to be stochastically stable with an induced
$\ell _{2}$
disturbance attenuation performance. Then the desired full- or reduced-order DOFCs are designed by using projection approach. Cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem. Finally, a numerical example is presented to show the effectiveness of the proposed methods.