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This article investigates stochastic stability of positive singular Markovian jump systems (PSMJSs) with mode-dependent derivative-term coefficient. Different from the existing results, the condition on stochastic stability of PSMJSs associated with state jumps behavior at switching instants is given by means of linear co-positive Lyapunuov function. On the basis of it, the conditions on stochastic stability under the cases of partially known transition rates and uncertain transition rates have been presented, respectively. All obtained conditions can be solved by linear programming (LP) technique. Finally, an example is introduced to illustrate the effectiveness and the merits of the results proposed in this article. [ABSTRACT FROM AUTHOR]

This study addresses the positive filter design problem for continuous‐time positive Markov jump linear systems (PMJLSs). Based on the necessary and sufficient condition for L1 ‐gain performance, two sufficient conditions to design positive full‐order and reduced‐order L1 ‐filters for PMJLSs are provided in terms of linear programming, respectively. A practical numerical example of an isotropic, homogeneous and unidimensional aquifer is presented at last to show the effectiveness of the proposed schemes. [ABSTRACT FROM AUTHOR]

This study introduces a problem of positive L1 filter design for positive piecewise homogeneous Markovian jump Takagi–Sugeno (T–S) fuzzy systems. The difference between the existing achievements is that the considered transition rate of the positive Markovian jump system is time‐varying. This time‐varying nature is finite piecewise homogeneous. The time variation of the transition rate is characterised by two cases: stochastic variation and arbitrary variation. First of all, sufficient conditions are obtained for stochastic stability and L1 performance under the transition rate in a manner of stochastic variation and arbitrary variation by means of choosing a linear co‐positive Lyapunov function. Then, based on the obtained achievements, the problem of positive L1 filter design for the positive piecewise homogeneous Markovian jump T–S fuzzy system is studied. All the mentioned problems in this study can be solved by linear programming. Finally, a biological model is proposed to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

This paper addresses the stochastic stability problem of positive Markov jump linear systems (PMJLSs). A necessary and sufficient condition of stochastic stability for PMJLSs is given which can be checked by solving linear programming feasibility problems due to the positivity property. A common co-positive Lyapunov function is constructed to solve the problem, and the equivalence among stochastic stability, 1-moment stability and exponential mean stability is proved afterwards. Considering the uncertain transition rates situation, PMJLSs with partially known transition rate matrix are investigated, and a necessary and sufficient condition for robust stochastic stability is proposed in linear programming form. Numerical examples are presented to show the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper presents a positive L 1 state-bounding observer which can estimate the state all the time for nonlinear positive Markovian jump systems. The considered system is represented by Takagi–Sugeno(T–S) fuzzy system. First of all, by constructing a linear co-positive Lyapunov function, the sufficient condition is obtained for stochastic stability and L 1 performance analysis respectively. Furthermore, a positive L 1 state-bounding observer for positive T–S fuzzy Markovian jump systems is designed. The conditions can be solved by linear programming. Finally, the results obtained are applied to the epidemiological model and illustrated to be better than the existing results by a numerical example. [ABSTRACT FROM AUTHOR]

This paper focuses on positive linear time-invariant systems with constant coefficients and specific exogenous disturbance. The problem of finding a hyper-pyramid to bound the set of the states that are reachable from the origin in the Euclidean space is addressed, subject to inputs whose ( 1 , 1 ) -norm or ( ∞ , 1 ) -norm is bounded by a prescribed constant. The Lyapunov approach is applied and a bounding hyper-pyramid is obtained by solving a set of inequalities. Iterative procedures (with an adjustable parameter) for reducing the hyper-volume of the bounding hyper-pyramid for the reachable set are proposed. [ABSTRACT FROM AUTHOR]