Robust and Adaptive Control Systems

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Robust and Adaptive Control Systems EEE8115-EEE8086 Robust and Adaptive Control Systems Chapter 3: The geometry of the state space This lecture will be recorded and you will be able to download it Dr Damian Giaouris http://www.staff.ncl.ac.uk/damian.giaouris/ EEE8044

Orthonormal Orthonormal basis for all vectors in the Cartesian PLANE

Orthogonal Orthogonal basis

General Basis

Conclusions Linear Dependant

HOS

State Space and Basis Vectors x 1 2 R2 3 R3 The state space is another vector space. We can define other bases. Can we find a “good” basis? A basis that consists of vectors that are invariant under the solution of the state equation. The invariance property means that if the solution at some point in time is on one of these vectors then it will remain on that vector for all subsequent times. This will greatly simplify our analysis. The purpose of this chapter is to explain how these bases can be found for second and third order systems. By doing that we can see how the state space is partitioned, and this will give us an easier geometric approach to study/control the system.