Output feedback control of Markovian jump repeated scalar nonlinear systems

This Chapter addresses the ℓ₂ dynamic output feedback (DOF) control design problem for Markovian jump repeated scalar nonlinear systems. The main contribution of this chapter can be summarized as: (1) The focused nonlinear system with a Markov process is novel, which is described by both a discrete-time state equation involving a repeated scalar nonlinearity and a Markovian jump system with finite discrete operation modes; The results obtained in this work will extend some of the results in [22] to the MJLs; (2) Based on the switching-sequence dependent Lyapunov function approach and the positive definite diagonally dominant Lyapunov function technique, a sufficient condition, which guarantees the considered system to be stochastically stable with an ℓ₂ disturbance attenuation performance, will be obtained, and to combat with matrix equalities in the condition, the developed algorithm of CCL procedure will be employed to cast the nonconvex feasibility problem into a sequential minimization problem subject to LMIs that can be readily solved by using standard numerical softwares; and (3) The desired full- and reduced-order DOF controllers are designed in a whole framework.