Filtering of Markovian Jump Repeated Scalar Nonlinear Systems

Abstract

In this chapter focus on the $\ell _2$-$\ell _{\infty }$ filter design problem for Markovian jump repeated scalar nonlinear systems. The main contributions of this chapter can be summarized as follows: (1) a novel nonlinear system model with a Markov process is introduced, which is described by a discrete-time state equation involving a repeated scalar nonlinearity that typically appears in recurrent neural networks and hybrid systems with finite discrete operation modes; (2) based on the mode-dependent positive definite diagonally dominant Lyapunov function approach, a sufficient condition is obtained, which guarantees that the corresponding filtering error system is stochastically stable and has a prescribed $\ell _{2}$-$\ell _{\infty }$ performance; (3) a sufficient condition for existence of admissible controllers is obtained in terms of matrix equalities, and a cone complementarity linearization (CCL) procedure is employed to transform a nonconvex feasibility problem into a sequential minimization problem subject to LMIs, which can be readily solved by existing optimization techniques; and (4) full- and reduced-order filters are designed in a unique framework.