This article presents a positivity analysis and exponential stabilization design for singular switched positive systems (SSPSs) with actuator saturation under a mode-dependent minimum dwell time (MDMDT) constraint. First, a necessary and sufficient positivity criterion is proposed for SSPSs using the singular value decomposition approach. Then, an exponential stability condition is provided for the closed-loop SSPSs via the mode-dependent state-feedback control using a novel discretized linear copositive Lyapunov function technique. Furthermore, by applying the matrix decomposition technique to the controller gain matrix and controller auxiliary gain matrix, an effective mode-dependent design scheme for a saturation controller in the solvable linear programming (LP) form is proposed for the SSPSs. For singular positive systems, an effective saturation control scheme in the solvable LP form can be obtained accordingly. Finally, three examples are provided to validate the results.

This article is concerned with the stochastic stability and$l_{1}$-gain control of two-dimensional (2-D) positive Markov jump systems (PMJSs) with directional delays based on the Roesser model. First, necessary and sufficient conditions (NSCs) for the stochastic stability of the addressed system are established by constructing a deterministic “equivalent” system and applying a stochastic copositive Lyapunov function. This reveals that the stochastic stability of 2-D PMJSs with delays is affected by the size of directional delays, the transition matrix, and system matrices. Second, the exact$l_{1}$-gain index is calculated and NSCs in the form of linear programming (LP) are established for the addressed system. Systematic methods for the$l_{1}$-gain controller design are proposed so that the closed-loop system (CLS) is positive and stochastically stable and has an optimal$l_{1}$-gain performance, which is achieved using an iterative algorithm and an analytical calculation method for a single-input case. Finally, the potency and accuracy of the theoretical results are verified using two examples.

This work discusses the fault detection problem for two-dimensional (2-D) positive systems (PSs) with distributed delays. First, a systematic method is proposed for the computation of exact values of $\ell _{1}$ -gain and $\ell _{-}$ index for delay-free systems, and the dimension expansion technique is used to transfer the computation of $\ell _{1}/\ell _{-}$ index for 2-D delayed PSs to one of the delay-free systems. Second, necessary and sufficient conditions are established such that the 2-D delayed PSs are asymptotically stable with a desired $\ell _{1}/\ell _{-}$ performance level (PL) $\gamma /\beta $ . Third, based on the above results, some NCSs are established such that the disturbance and the fault impact on the output signal are minimized and maximized, respectively. An algorithm (iterative) is formulated for the solution of the convex optimization problem. Finally, the potency and accuracy of the developed theoretical results are exhibited by an example.