Solution of State Eqs when A matrix is Time dependent

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SUMMARY

The discussion focuses on solving state equations of the form dx/dt = A x + bu, where the matrix A has time-dependent elements. The user initially struggles with this problem, as traditional methods apply only when A is constant. A solution is provided through a reference to a Wikibooks page that outlines methods for handling time-variant systems. This resource offers specific techniques for obtaining solutions when A is not constant.

PREREQUISITES
  • Understanding of state-space representation in control systems
  • Familiarity with matrix exponentiation and its application in differential equations
  • Knowledge of time-variant systems in control theory
  • Basic proficiency in linear algebra
NEXT STEPS
  • Study the methods for solving time-variant state equations as outlined in the provided Wikibooks link
  • Explore the concept of matrix exponentiation in detail for time-dependent matrices
  • Learn about the Lyapunov's direct method for stability analysis in time-variant systems
  • Investigate numerical methods for simulating time-variant systems using software like MATLAB or Python
USEFUL FOR

Control engineers, systems analysts, and students studying dynamic systems who need to solve time-dependent state equations effectively.

Barkan
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Hi all,

I am struggling to solve some simple state equations in the following form.

dx/dt = A x + bu

solution is simple if A has only constant elements, because i can multiply both sides with exp(-At) and solve.

in my case, A has time dependent elements. i know their functions. is there any particular solution for this case?

thank you in advance.
 
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