Observability and Geometric Approach of 2D Hybrid Systems

International Journal of Computers ◽

10.46300/9108.2021.15.18 ◽

2021 ◽

Vol 15 ◽

pp. 115-122

Author(s):

Tiberiu Vasilache ◽

Valeriu Prepelita

Keyword(s):

Systems Theory ◽

Hybrid Systems ◽

Geometric Approach ◽

Geometric Characterization ◽

2D Systems ◽

Special Regard ◽

Observability Gramian

A connection is emphasized between two branches of the Systems Theory, namely the Geometric Approach and 2D Systems, with a special regard to the concept of observability. An algorithm is provided which determines the maximal subspace which is invariant with respect to two commutative matrices and which is included in a given subspace. Observability criteria are obtained for a class of 2D systems by using a suitable 2D observability Gramian and some such criteria are derived for LTI 2D systems, as well as the geometric characterization of the subspace of unobservable states. The presented algorithm is applied to determine this subspace.

Download Full-text

Topics in 2D Systems Theory

Systems, Models and Feedback: Theory and Applications ◽

10.1007/978-1-4757-2204-8_9 ◽

1992 ◽

pp. 95-110

Author(s):

Ettore Fornasini ◽

Giovanni Marchesini

Keyword(s):

Systems Theory ◽

2D Systems

Download Full-text

Synthesis, physicochemical, rheological and in-vitro characterization of double-crosslinked hyaluronic acid hydrogels containing dexamethasone and PLGA/dexamethasone nanoparticles as hybrid systems for specific medical applications

International Journal of Biological Macromolecules ◽

10.1016/j.ijbiomac.2018.12.181 ◽

2019 ◽

Vol 126 ◽

pp. 193-208 ◽

Cited By ~ 13

Author(s):

Zohre Mousavi Nejad ◽

Bahman Torabinejad ◽

Seyed Mohammad Davachi ◽

Ali Zamanian ◽

Sadaf Saeedi Garakani ◽

...

Keyword(s):

Hyaluronic Acid ◽

Hybrid Systems ◽

Medical Applications ◽

In Vitro Characterization

Download Full-text

Theory of hybrid dynamical systems and its applications to biological and medical systems

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2010.0237 ◽

2010 ◽

Vol 368 (1930) ◽

pp. 4893-4914 ◽

Cited By ~ 65

Author(s):

Kazuyuki Aihara ◽

Hideyuki Suzuki

Keyword(s):

Nonlinear Dynamics ◽

Dynamical Systems ◽

Mathematical Modelling ◽

Systems Theory ◽

Control Systems ◽

Hybrid Systems ◽

Hybrid Dynamical Systems ◽

Medical Systems ◽

Theme Issue ◽

And Control

In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on–off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.

Download Full-text