Sliding-mode H ∞ ${H_{\infty}}$ synchronization for complex dynamical network systems with Markovian jump parameters and time-varying delays

Abstract

This paper is devoted to the investigation of the sliding-mode controller design problem for a class of complex dynamical network systems with Markovian jump parameters and time-varying delays. On the basis of an appropriate Lyapunov-Krasovskii functional, a set of new sufficient conditions is developed which not only guarantee the stochastic stability of the sliding-mode dynamics, but also satisfy the H ∞ performance. Next, an integral sliding surface is designed to guarantee that the closed-loop error system reach the designed sliding surface in a finite time. Finally, an example is given to illustrate the validity of the obtained theoretical results.

Stabilization of Semi-Markovian Jumping Uncertain Complex-valued Networks with Time-varying Delay: A Sliding-Mode Control Approach

“…In order to overcome this problem, we choose an appropriate Lyapunov-Krasovskii functionals without using the delay-decomposition technology and the free variable method. Some sufficient and less conservative results can be proposed compared with those in [39,40]. When the considered systems are transformed into the general complex networks, the number of decision various in our results is 7n 2 + 9n + 2mn.…”

“…Remark 5. It should be mentioned that, compare with the literature [39], in this paper, the designed sliding mode controller is more general because of the proposed sliding mode controller requires the involved matrix D li must be square matrix, while mine not. Moreover, the designed sliding mode controller also contains the matrices M i and N i , which further illustrates the system parameter uncertainties have a great impact on the the designed sliding mode controller.…”

“…When the considered systems are transformed into the general complex networks, the number of decision various in our results is 7n 2 + 9n + 2mn. However, for the existing literatures [39,40] without external disturbance and Markovian switching, the number of decision various is 12.5n 2 + 14.5n + 3mn and 7n 2 + 9.5n + 2.5mn, respectively. From this point of view, it was obvious that our results are less conservative in terms of computational complexity.…”

“…As is well-known that for the obtained the linear matrix inequalities, the computational complexity depends on the maximum number of decision variables, which sometimes brings time complexity in the process of solving. It is noteworthy that there are two common types of methods in the existing literature: the free variable method [39] and the Lyapunov-Krasovskii functionals [40], which will lead to the number of decision variables becomes large. At the same time, the corresponding computational burden will increase.…”

Stabilization of Semi-Markovian Jumping Uncertain Complex-Valued Networks with Time-Varying Delay: A Sliding-Mode Control Approach

“…It should be mentioned that, compare with the literature [44], in this paper, the designed sliding mode controller is more general because of the proposed sliding mode controller requires the involved matrix D li must be square matrix, while mine not. Moreover, the designed sliding mode controller also contains the matrices M i and N i , which further illustrates the system parameter uncertainties have a great impact on the the designed sliding mode controller.…”