Search

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 study is concerned with H ∞ control problems for positive systems with time delays using dynamic output feedback. Novel bounded real lemma for continuous‐time systems with time delays is first presented, which shows one of the remarkable properties of diagonal positive definite matrix solutions to linear matrix inequalities for positive systems. The proposed results reveal that H ∞ norms of positive systems with time delays in state and output equations are equivalent to that of the corresponding systems with zero delays. The positivity preserving H ∞ control problem by means of dynamic output feedback is also considered, and thus necessary and sufficient conditions in the forms of matrix equalities are established for the solvability of such problem. The desired controller gains can be obtained by means of cone complementarity linearisation techniques. A numerical example is finally given to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]