Stability and stabilization of periodic piecewise positive systems: A time segmentation approach

This paper focuses on two main aspects. Firstly, we introduce a generalized form of conformable fractional derivatives called ‐conformable fractional derivatives along with their corresponding integrals . We also present several theorems related to these derivatives. Secondly, we investigate the observability, controllability, and stability of a fractional dynamical system known as the ‐conformable fractional dynamical system ( ‐CF‐DS). We establish the connection between controllability, the controllability matrix, and the fractional ‐conformable fractional differential Lyapunov equation ( ‐CF‐DLE). We prove that the ‐CF‐DS is stable if and only if all eigenvalues of the matrix have negative real parts. Moreover, we provide theorems regarding the observability of an ‐CF‐DS. To demonstrate the efficacy of our results, we include illustrative examples.

Controllability, observability, and stability of φ‐conformable fractional linear dynamical systems

Sadek

2024

Probability rate optimization of positive Markov jump linear systems via DC programming

Zhao,

Zhu,

Ogura

et al. 2024

We investigate the stabilization problem of positive Markov jump linear systems by optimizing their transition probability rates. By using the convex property of posynomials and the standard mathematical programming that deals with the difference in convex functions, we show that transition probability rate synthesis problems can be solved via difference‐of‐convex (DC) programming. A numerical example is used to illustrate the effectiveness of our results.

Stochastic convergence to recurrent state equilibrium for state‐based games

Wei,

2024

State‐based games contain an additional state space by comparing with normal games. Correspondingly, the equilibrium of state‐based games is called recurrent state equilibrium (RSE). For state‐based games, the stochastic convergence to RSE is investigated in this paper. Firstly, the stochastic convergence of state‐based games is defined. Then, a kind of state‐based best‐response update rule is designed for state‐based games. Under this update rule, the state‐based games can be converted into the Markovian switching logical networks through the semi‐tensor product. Next, based on the results of Markovian switching logical networks and positive systems, the stochastic convergence of state‐based games is investigated and a verifiable criterion is derived. Finally, an example is presented to illustrate the validity of the obtained criterion.