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First, an adaptive distributed observer is designed to estimate both the system matrix and the state of the leader system.
Particularly, two different Markov processes are considered for modeling the randomness of system matrix and the state delay.
They can be efficiently solved by Krylov subspace methods, as here the main ingredient is the multiplication with the system matrix and the application of the preconditioner.
Many model predictive control (MPC) algorithms have been proposed in the literature depending on the conditionality of the system matrix and the choice of its cost-function.
The elements of both the system matrix and the measurement matrix are allowed to be random variables in order to reflect the reality.
For the actuator fault reconstruction scheme, a virtual system comprising the system matrix and a fixed input distribution matrix is used for the design of the observer.
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Sets of slack variables are adopted to decouple the product terms between system matrices and Lyapunov matrices.
Polytopic uncertainties both in system matrices and transition probability matrices of Markov process are taken into consideration.
In sufficient conditions, we introduce some additional scalar matrix variables to realize the decoupling between the filtering error system matrices and Lyapunov matrices.
The uncertain stochastic system with Markovian switching under consideration involves parameter uncertainties both in the system matrices and in the mode transition rates matrix.
The uncertain Markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix.
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