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In this paper, the positive observer design problem is considered for a class of positive delayed Markovian jump systems (PDMJSs). Firstly, a necessary and sufficient condition is established to check the positivity of delayed Markovian jump systems (DMJSs). Then, necessary and sufficient conditions for PDMJSs being asymptotically mean stable are established to be independent of time delay. Based...
In this paper, using semi-tensor product and the vector form of Boolean logical variables, the asynchronous Boolean networks under different update schemes are converted into probabilistic discrete time dynamic systems, and the structure matrix of discrete time dynamic systems is a probabilistic transaction. It provides a new way to study the properties of random Boolean networks. Under this framework,...
The paper deal with problems on stability of Boolean networks with respect to a given part of variables characterizing the Boolean network. Using semi-tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean network can be converted to a discrete time linear dynamics, called the algebraic form of the Boolean network. Main results consist of two parts: (i) From the algebraic...
In this paper, the uniform stability in one part of the variables for probabilistic Boolean networks is discussed. Firstly, definition of partial stability of probabilistic Boolean networks is introduced. Using semi-tensor product, the probabilistic Boolean network is converted to its algebraic form. From the algebraic form of probabilistic Boolean network, necessary conditions are obtained from the...
The concept of canalizing Boolean function is generalized to multi-input multi-output canalizing Boolean mapping. Using the semi-tensor product of matrices and the matrix expression of logical functions, an easily verifiable condition is provided for testing whether a Boolean mapping is a canalizing Boolean mapping. Using it, the disturbance decoupling problem (DDP) of Boolean control networks is...
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