Finite-Time Stability of Discrete Autonomous Systems

Fixed-time Stability of Discrete-time Autonomous Systems

“…Note that S k ě 0, @k ą K 1 and based on ( 20) and ( 35), one has S k`1 ď S k . Based on (36), when S k " 1, then S k`1 " 0. Therefore, for a fixed time K 2 where S K 2 ´1 " 1, one has S K 2 " 0.…”

“…While most real-world systems are CT in nature, DT systems are of great importance since systems are typically discretized and controlled with digital computers and micro-controllers in real-world applications. Even though finite-time stability of DT is studied in [15], [16], [35], [36], fixed-time stability of DT systems is surprisingly unsettled, despite its practical importance. This gap motivates us to present fixed-time Lyapunov stability conditions that pave the way for realization of fixed-time control and identification of DT systems through designing appropriate controllers and adaptation laws, respectively.…”

Adaptive controller design for fixed‐time bipartite consensus of multi‐agent systems with disturbances

“…The second eigenvalue of the Interaction Laplace matrix, called algebraic connectivity, can determine the rate of convergence of MASs, which is proved in Reference 11. In addition, some research results of appropriately designing interaction graphs to increase algebraic connectivity are also obtained in Reference 7. These efforts mainly lead to asymptotic convergence, which means that agreement can be reached only when time approaches infinity in References 5 and 12.…”

“…On the other hand, the consensus problem of finite‐time has been generalized. In order to achieve faster convergence, the regularity of Lyapunov function and settlement function in the stability analysis of finite time autonomous system are linked in Reference 7. Meanwhile, the control idea of finite time was extended in Reference 5, and MASs with single integral dynamics was developed in Reference 8.…”

“…In summary, we propose two fixed‐time bipartite consensus algorithms for algebraic connected graphs. The main contributions of this article are as follows: (i) Different from References 5, 7, 8, and 12, we ensure that all agents reach an agreement with or without disturbances, under a fixed time bipartite protocol. (ii) Compared with References 14, 16, and 20, under the established algorithm, when the control input parameters change with time, all agents have the ability to converge to the expected bounded time state.…”