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This article is concerned with the problem of output feedback control for a class of continuous-time hidden semi-Markov jump systems with time delays. Due to the limitations of the actual environment, system modes are usually undetectable, which are called hidden modes. The controller modes are described as observable modes. Emission probabilities are used to establish the relationship between abovementioned two concepts. The jump parameters are governed by the hidden semi-Markov process, which can better describe the asynchronous information between the controller modes and the system modes. Besides, time delays are considered to be time-varying and dependent on the hidden modes. By employing some mathematical transformation and constructing a novel Lyapunov–Krasovskii functional, some new parameter-dependent sufficient stabilization conditions can be obtained by designing an observed-mode-dependent static output-feedback controller. Finally, a practical example is provided to illustrate the effectiveness and merits of the proposed methods. [ABSTRACT FROM AUTHOR]

In this article, the passivity-based control problem is addressed for hidden Markov jump systems with singular perturbations and partially unknown probabilities. The hidden Markov model (HMM) with partially unknown probabilities is introduced, where the partially unknown probabilities may exist in either the transition probability matrix of Markov chain, the observation probability matrix of observed signal, or in both of them. Thus, the underlying HMM is more general than the one in some existing works. By using this HMM, some passivity analysis criteria are established for Markov jump singularly perturbed systems with partial unknown probabilities. Based on these criteria, a unified method is presented for the design of controllers to ensure the passivity of the system. A numerical example and an armature controlled dc motor model are given to illustrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The slow state variables feedback stabilization problem for semi-Markov jump discrete-time systems with slow sampling singular perturbations is discussed in this work. A new fairly comprehensive system model, semi-Markov jump system with singular perturbations, which is more general than Markov jump model, is employed to describe the phenomena of random abrupt changes in structure and parameters of the systems. Based on a slow state variables feedback control scheme, a novel technique to design the desired controller is presented and the allowed maximum of singular perturbation parameter can be calculated. With the help of the discrete-time semi-Markov kernel approach, some sojourn-time-dependent and less-conservative sufficient conditions are established via a novel matrix decoupling technique to ensure the solvability of the problem to be addressed. Finally, an illustrative example is given to show the superiority and usefulness of the proposed method. [ABSTRACT FROM AUTHOR]