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This work deals with a class of nonlinear dynamical systems exhibiting both continuous and discrete dynamics, which is called as hybrid dynamical system.
We provide a broader framework of generalized hybrid dynamical systems allowing us to handle issues on modeling, stability and interconnections.
Various sufficient stability conditions are proposed by extensions of direct Lyapunov method.
We also explicitly show Lyapunov formulations of the nonlinear small-gain theorems for interconnected input-to-state stable hybrid dynamical systems.
Applications on modeling and stability of hybrid dynamical systems are given by effective strategies of vaccination programs to control a spread of disease in epidemic systems.
In this thesis stability and robustness properties of systems of functional differential equations which dynamics depends on the maximum of a solution over a prehistory time interval is studied. Max-operator is analyzed and it is proved that due to its presence such kind of systems are particular case of state dependent delay differential equations with piecewise continuous delay function. They are nonlinear, infinite-dimensional and may reduce to one-dimensional along its solution. Stability analysis with respect to input is accomplished by trajectory estimate and via averaging method. Numerical method is proposed.