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Summary: In this paper, the problem of state and fault estimations for a class of linear time‐delay systems is studied, whose state and output are affected by delays and unknown disturbances. To solve this problem, two methods of observer design are proposed in this paper. One is a new sliding mode observer (SMO) based on proper system transformation and H∞$$ {H}_{\infty } $$ filter, the H∞$$ {H}_{\infty } $$ asymptotic stability of state and fault estimation error can be guaranteed. The second one is an adaptive sliding‐mode unknown input observer (ASMUIO), which is developed under the medium rank of the perturbation distribution matrix to estimate the disturbance simultaneously with the state and fault, and then to eliminate the disturbance effect from the estimation error systems. The conditions for the existence of the proposed SMO and ASMUIO and the strict proof of their feasibility are presented. Two numerical examples are given to illustrate the effectiveness of the new methods. [ABSTRACT FROM AUTHOR]

This paper mainly studies the generalized H2 control of discrete‐time semi‐Markov jump systems with bounded sojourn‐time. By constructing the mode‐dependent Lyapunov function related to the elapsed‐time and the semi‐Markov process, we obtain sufficient conditions to ensure the σ‐error mean square stable and generalized H2 performance of the semi‐Markov jump system. Moreover, by introducing slack variables, the generalized H2 performance index is reduced and the feasible region is expanded. Finally, through numerical calculations, we confirm the effectiveness of the design methods. [ABSTRACT FROM AUTHOR]

In this paper, a class of non-autonomous stochastic Nicholson's blowflies systems with patch structure and time delays is formulated and studied. By constructing suitable Lyapunov functions and using the stochastic technical, the pth moment boundedness and almost sure growth bounds are discussed, which reveal that solutions of the system do not exceed the time value t and the sample Lyapunov exponent is no more than zero. Then, the system is proved to be exponentially stable (or extinct) if the production rate is less than the mortality rate, which provides an effective reference for the population control. Moreover, taking into account the specific form of time-varying coefficients, related results for several classical stochastic Nicholson's blowflies systems are studied, and they show the significant improvement of this paper. Finally, numerical simulations for several specific examples are carried out to illustrate our theoretical conclusions. [ABSTRACT FROM AUTHOR]

This article studies a class of asynchronous generalized H2 control problems for continuous‐time discrete‐state semi‐Markov jump linear systems. By constructing a Lyapunov function based on the semi‐Markov process, introducing a weak infinitesimal operator and applying the smoothness of the expectation, sufficient conditions are obtained to ensure stochastic stability and generalized H2 performance of the system. Simultaneously, equivalent conditions are given by introducing slack variables and an asynchronous controller is designed. Moreover, we derive the sufficient conditions for the case where the transition rate is partially unknown. Finally, we use the cone complement linearization iterative algorithm to simulate two examples to prove the effectiveness of the design scheme. [ABSTRACT FROM AUTHOR]