# Registered Data

Contents

- 1 [CT192]
- 1.1 [02459] Functional ODE observers for DAE control systems
- 1.2 [01281] Optimal network synchronization from a higher-order topological approach
- 1.3 [02295] Optimal network synchronization from a higher-order topological approach
- 1.4 [00348] Design of control for IT2 fuzzy stochastic systems with multi disturbances

# [CT192]

## [02459] Functional ODE observers for DAE control systems

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Many control systems have essential features, which can only be expressed if system dynamics is described by simultaneous differential and algebraic equations (DAEs). For example, the classical state space models, governed only by ordinary differential equations (ODEs), cannot adequately treat impulses that occur in electrical circuits. This talk is devoted to the problem of designing functional observers for linear DAEs. A new and milder sufficient condition for functional observers is proved.**Classification**:__93B53__,__93B07__,__93A10__,__93C99__,__93D05__**Author(s)**:**Nutan Kumar Tomar**(Indian Institute of Technology Patna)- Juhi Jaiswal (Indian Institute of Technology Madras)
- Pabitra Kumar Tunga (Indian Institute of Technology Patna)

## [01281] Optimal network synchronization from a higher-order topological approach

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In this talk, we will discuss the optimal network synchronization problem. The totally homogenous network approach will be reviewed, and a higher-order topological approach will be introduced, with some preliminary results reported.**Classification**:__93B70__,__34D06__,__57Q05__**Author(s)**:**Guanrong (Ron) Chen**(City University of Hong Kong )

## [02295] Optimal network synchronization from a higher-order topological approach

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: In tis talk, we consider a connected, undirected and unweighted continuous-time network of a finite number of homogeneous node systems. The issue of network synchronization will be addressed based on spectral analysis and algebraic topology theory. It has been well known since 2002 that the synchronizability of such a network is determined by the network Laplacian matrix in terms of its smallest nonzero eigenvalue [1] or the ratio of the largest eigenvalue over the smallest nonzero eigenvalue [2]. To search for optimal network topologies with the best possible synchronizability, it was found [3] that, in any group of comparable networks of the same size (i.e., with same number of nodes and same number of edges), the totally homogeneous network has the best possible synchronizability. A totally homogeneous network is characterized by the degree, girth and path-sum of its nodes, which are defined as follows: (i) degree of a node is the number of its edges; (ii) girth of a node is the number of edges within a shortest cycle passing through this node; (iii) path-sum of a node is the total number of edges from all other nodes to this node through their shortest paths respectively (i.e., the average distance after dividing by the total number of nodes). A totally homogeneous network is defined as one with same node degree, same girth and same path-sum within a group of comparable networks, which was found [3] to have the best synchronizability in the group. It was also observed [3] that all optimal totally homogeneous networks are uniformly and symmetrically connected, with many cycles of different orders. In algebraic topology, cycles are higher-order topological structures, belonging to various-order simplices such as nodes, edges, triangles, tetrahedrons and so on, including higher-order cavities [4]. In algebraic topology, there are important measures of Betti numbers and Euler characteristic index, which describe the relationships among various-order simplices in a complex network. By examining four common types of complex networks: regular networks, small-world networks, random-graph networks and totally homogeneous networks, it was found [4] that the synchronizability of these networks has the following ranking: totally homogeneous networks are better than random-graph networks, which are better than small-world networks, which in turn are better than regular networks. This synchronizability ranking is consistent with other reports in the literature, and is supported by all the criteria based on Laplacian eigenvalues and Betti numbers, as well as the Euler characteristic number. According to our extensive simulations and observations, among all available criteria the Euler characteristic index is the best criterion to use for determining and ranking the network synchronizability. References [1] X. F. Wang and G. Chen, “Synchronization in scale-free dynamical networks: Robustness and fragility,” IEEE Trans. Circuits Syst.-I, Fundam. Theory Appl., vol. 49, no. 1, pp. 54-62, 2002. [2] M. Barahona and L. M. Pecora, “Synchronization in small-world systems,” Phys. Rev. Lett., vol. 89, no. 5, Art. no. 54101, 2002. [3] D. H. Shi, G. Chen, W. W. K. Thong, and X. Y. Yan, “Searching for optimal network topology with best possible synchronizability,” IEEE Circuits Syst. Mag., vol. 13, no. 1, pp. 66–75, 1st Quart., 2013. [4] D. H. Shi, L. Y. Lü, and G. Chen, “Totally homogeneous networks,” Nat. Sci. Rev., vol. 6, no. 5, pp. 962–969, 2019.**Classification**:__93B70__,__34D06__,__57Q05__**Author(s)**:**Guanrong (Ron) Chen**(City University of Hong Kong )

## [00348] Design of control for IT2 fuzzy stochastic systems with multi disturbances

**Session Date & Time**: 2E (Aug.22, 17:40-19:20)**Type**: Contributed Talk**Abstract**: Anti disturbance control design problem is proposed for a class of interval type-2 fuzzy stochastic systems subject to uncertainty and multiple disturbances. A fuzzy exogenous system considers a new fuzzy disturbance observer to precisely evoke the properties of interval type 2 fuzzy stochastic models with multiple disturbances. In order to ensure the stochastic stability of the closed-loop fuzzy system, a new sufficient condition is constructed using the method of linear matrix inequalities by integrating the $\textit{Ito}$ operator and choosing the appropriate Lyapunov-Krasovskii functional candidate dissipativity performance index. Finally, the provided theory is demonstrated with the example.**Classification**:__93Bxx__,__93Exx__,__93Dxx__**Author(s)**:**Aarthi Subramanian**(Research Scholar, Anna University Regional Campus Coimbatore)- Marshal Anthoni S (Anna University Regional Campus Coimbatore)