General Stability Bounds in Perturbed Systems

  • Alexander Weinmann


Solving the linear first-order time-varying differential equation the
$$\dot x(t) = a(t)x(t) + u(t)$$
homogeneous differential equation
$$\dot x(t) = a(t)x(t){\rm{ or }}\frac{{\dot x(t)}}{{x(t)}} = \frac{d}{{dt}}\ln x(t) = a(t)$$
is considered first.
$$In{\rm{ }}x(t) = \int_{{t_o}}^t {a(\tau } ) + \ln {\rm{ }}k$$
$$x(t) = k{\rm{ exp }}\int_{{t_o}}^t {a(\tau )d\tau \underline{\underline \Delta } } k\varphi (t,{t_o})$$


Feedback Controller State Feedback Controller Lyapunov Equation Output Feedback Controller Homogeneous Differential Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Wien 1991

Authors and Affiliations

  • Alexander Weinmann
    • 1
  1. 1.Department of Electrical EngineeringTechnical University ViennaAustria

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