Abstract
The singular systems, which could widely describe more general systems and present traits of physical features, are discussed in this study. Taking the fact that noises always exist in the state and output measurement of one singular system into consideration, which may cause some errors and decrease system performance, this article devotes itself to the dissipative control for discrete-time singular Markov jump systems (SMJSs) with multiplicative noises. To deal with the asynchronous phenomena between the system modes and the controller modes, a set of Markov chains are constructed. To make sure the closed-loop singular system is dissipative, a set of sufficient conditions are derived based on the linear matrix inequalities, and then the asynchronous controller is designed to ensure that SMJSs are stochastically admissible and strictly dissipative. Finally, a simulation example is carried out to verify the correctness of the derived theorem. The designed asynchronous controller improves the robustness of the controller and overcomes the asynchronous phenomenon. This control method can be applied in the fields of robot control system.
Highlights
Many dynamic systems subjected to abrupt change of environment and failure of system following the rule of Markov jump process, containing stochastic process and Markov chain-based constrained modes, are called Markov jump systems, which can be used to describe real systems with sudden change or modes switching among structure and parameters
The problem of asynchronous dissipative control for singular discrete-time Markov jump system with multiplicative noises is investigated by Lyapunov function approach together with linear matrix inequalities (LMIs) technique in this article
To reflect more practical plant, the state and output multiplicative noises are introduced and a linear transformation technique is applied to deal with these multiplicative noises
Summary
Many dynamic systems subjected to abrupt change of environment and failure of system following the rule of Markov jump process, containing stochastic process and Markov chain-based constrained modes, are called Markov jump systems, which can be used to describe real systems with sudden change or modes switching among structure and parameters. Finite-time asynchronous H1 control problem for Markov jump systems was studied by Chen et al.[30]. The investigated system is a kind of finite piecewise homogeneous Markov jump system For such a system, an asynchronous controller is designed as follows: uðkÞ 1⁄4 K dðkÞ xðkÞ ð4Þ. In theorem 2, an asynchronous state feedback controller is designed and the sufficient condition of closedloop is derived to ensure the SMJs with multiplicative noises are stochastically admissible and strictly dissipative. System (8) under zero initial status with uðkÞ 1⁄4 0 is regarded as stochastically admissible and strictly dissipative, if there exists a positive scalar a > 0 and symmetric matrices Pip > 0; the following
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
