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An additional condition called "properness" or "radial unboundedness" is required in order to conclude global stability. Global asymptotic stability (GAS) follows similarly. It is easier to visualize this method of analysis by thinking of a physical system (e.g. vibrating spring and mass) and considering the energy of such a system. If the ...
For asymptotic stability, the state is also required to converge to =. A control-Lyapunov function is used to test whether a system is asymptotically stabilizable , that is whether for any state x there exists a control u ( x , t ) {\displaystyle u(x,t)} such that the system can be brought to the zero state asymptotically by applying the ...
ISS unified the Lyapunov and input-output stability theories and revolutionized our view on stabilization of nonlinear systems, design of robust nonlinear observers, stability of nonlinear interconnected control systems, nonlinear detectability theory, and supervisory adaptive control. This made ISS the dominating stability paradigm in ...
If ˙ is negative definite, then the global asymptotic stability of the origin is a consequence of Lyapunov's second theorem. The invariance principle gives a criterion for asymptotic stability in the case when V ˙ ( x ) {\displaystyle {\dot {V}}(\mathbf {x} )} is only negative semidefinite.
In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation , for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature ...
In control theory, a continuous linear time-invariant system (LTI) is exponentially stable if and only if the system has eigenvalues (i.e., the poles of input-to-output systems) with strictly negative real parts (i.e., in the left half of the complex plane). [1]
Cardiac physiology or heart function is the study of healthy, unimpaired function of the heart: involving blood flow; myocardium structure; the electrical conduction system of the heart; the cardiac cycle and cardiac output and how these interact and depend on one another.
The conduction system consists of specialized heart muscle cells, situated within the myocardium. [3] There is a skeleton of fibrous tissue that surrounds the conduction system which can be seen on an ECG. Dysfunction of the conduction system can cause irregular heart rhythms including rhythms that are too fast or too slow.