A novel full-order and reduced-order fault detection filters design method for continuous-time singular Markov jump systems with complexity transition rates

This work is concerned with the problem of full-order and reduced-order fault detection filters (FDFs) design in a convex optimization frame for continuous-time singular Markov jump systems (CTSMJSs) with complexity transition rates (TRs). A novel Lyapunov function construct approach is utilized to cope with the stochastic admissibility problem for CTSMJSs with complexity TRs. In order to obtain effective full-order and reduced-order FDFs, we decoupled the inequality using the presupposed Lyapunov matrix. Owing to the use of Lyapunov stochastic admissibility theory and a novel decoupling method based on convex polyhedron technique, some sufficient conditions are obtained to guarantee that the resulting full-order and reduced-order FDFs are suitable for CTSMJSs with complexity TRs. In particular, the reduced-order FDF has the advantages of small storage space and fast detection speed compared with the full order FDF. Four illustrative examples are given to explain the effectiveness of the proposed full-order and reduced-order FDFs design method.

Stochastic Admissibility for a Class of Nonlinear Singular Markovian Jump Systems with Time-Delay and Partially Unknown Transition Probabilities

The problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay and partially unknown transition probabilities is discussed in this note. The considered singular matrices Er(t) in the discussed system are mode-dependent. By using the free-weighting matrix method and the Lyapunov functional method, a sufficient condition which guarantees the considered system to be stochastically admissible is presented in the form of linear matrix inequalities(LMIs). Finally, a numerical example is given to show the effectiveness of the presented method.

Stochastic Admissibility for a Class of Nonlinear Singular Markovian Jump Systems with Time-Delay

This paper is concerned with the problem of the stochastic admissibility for a class of nonlinear singular Markovian jump systems with time-delay by employing the free-weighting matrix method and the Lyapunov functional method. The singular matrices Er(t)in the discussed system are mode-dependent. A sufficient condition is presented to guarantee the considered system to be stochastically admissible. The proposed result is formulated in terms of linear matrix inequalities(LMIs). A numerical example is provided to verify the effectiveness of the obtained method.