Abstract
In this work, the result of reachable set bounding and extended dissipative control synthesis of the Markovian jump time-delayed system is studied subject to stochastic actuator failures and partially known transition probabilities. Specifically, a novel actuator fault model is designed, in which the actuator fault matrix satisfies a certain probabilistic condition. Under the construction of an appropriate Lyapunov–Krasovskii functional (LKF), as well as reciprocal convex approach, Jensen’s integral inequality, and reachable set lemma, delay-dependent sufficient criteria are obtained in terms of linear matrix inequalities (LMIs) for finding an ellipsoid to bound the reachable sets of the Markovian jump time-delayed system with bounded disturbances. Finally, two numerical examples are provided to validate the effectiveness of the proposed strategy.
Highlights
Markovian jump systems are a kind of stochastic switched systems, in which the switching between multiple modes is governed by a stochastic process described by a Markov chain
Markovian jump systems are appropriate model systems with random abrupt variations, which may be due to malfunction of machine in manufacturing systems, fluctuations in operating points, and environmental disturbances [1,2,3,4,5]. erefore, a remarkable progress has been made in the study of Markovian jump systems and has proved its successful applications in chemical systems, economic systems, power systems, electrical circuit systems, and so on [6,7,8,9]
We have investigated the reachable set bounding and extended dissipative controller synthesis of time-delayed Markovian jump systems with partially known transition probabilities and stochastic actuator failures and bounded disturbances
Summary
Markovian jump systems are a kind of stochastic switched systems, in which the switching between multiple modes is governed by a stochastic process described by a Markov chain. (i) e concept of extended dissipative and reachable set estimation is successfully first time applied to Markovian jump time-delayed systems with partially known transition probabilities and bounded disturbances (ii) We have investigated the result of the extended dissipative analysis and stochastic fault-tolerant control design for a class of Markovian jump systems where the transition rate matrix satisfies the partially known probability conditions (iii) Under the appropriate LKF, Jensen’s integral inequality and the reciprocal convex approach, a new set of sufficient conditions is obtained in the form of LMIs to guarantee the Markovian jump timedelayed system bounded by an ellipsoid and satisfies the extended dissipative performance index (iv) Two numerical simulation demonstrate the feasibility and effectiveness of the proposed approach e remaining part of this work is constructed as follows. P > 0( ≥ 0) means that P is real, symmetric, and positive definite (positive semi-definite); I is the identity matrix of appropriate dimension; the notation E[·] stands for the expectation operator; and “∗” is used to represent a term that is induced by symmetry
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