Stabilizing control for linear systems with bounded parameter and input uncertainty

  • S. Gutman
  • G. Leitmann
Optimal Control Stochastic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 41)


We consider dynamical systems with norm-bounded uncertainty in (i) the system parameters (model uncertainty) or in (ii) the input (disturbance).

For case (i), the nominal (null uncertainty) system is linear with constant matrices. Such systems with norm-bounded control as well as with a control penalty are treated. However, in the former the treatment is restricted to single input systems in companion form, and in the latter to second order systems. For case (ii), the system is linear with time-varying matrices and norm-bounded control.

Using some results from the theories of differential games and general dynamical systems, we deduce feedback controls which render the origin uniformly asymptotically stable in the large for all admissible parameter uncertainties or input disturbances; these may be both time and state dependent.

The application of the theory is illustrated by examples.


Feedback Control Parameter Uncertainty Differential Game Input Disturbance Input Uncertainty 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1976

Authors and Affiliations

  • S. Gutman
    • 1
  • G. Leitmann
    • 2
  1. 1.NASAAmes
  2. 2.University of CaliforniaBerkeley

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