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Prin ter: Opaque this
A Course in Robust
Con trol Theory
a con v ex approac h
Geir E. Dullerud F ernando G. P aganini
Univ ersit y of Illinois Univ ersit y of California
Urbana-Champaign Los Angeles
This is page i
Prin ter: Opaque this
Con ten ts
0 In tro duction 1
System represen tations . . . . . . . . . . . . . . . . . . . 2
Blo c k diagrams . . . . . . . . . . . . . . . . . . . 2
Nonlinear equations and linear p ositions . . 4
Robust con trol problems and uncertain t y . . . . . . . . . 9
Stabilization . . . . . . . . . . . . . . . . . . . . . 9
Disturbances mands . . . . . . . . . . . . 12
Unmo deled dynamics . . . . . . . . . . . . . . . . 15
1 Preliminaries in Finite Dimensional Space 18
Linear spaces and mappings . . . . . . . . . . . . . . . . 18
V ector spaces . . . . . . . . . . . . . . . . . . . . 19
Subspaces . . . . . . . . . . . . . . . . . . . . . . 21
Bases, spans, and linear indep endence . . . . . . 22
Mappings and matrix represen tations . . . . . . 24
Change of basis and in v ariance . . . . . . . . . . 28
Subsets and Con v exit y . . . . . . . . . . . . . . . . . . . 30
Some basic top ology . . . . . . . . . . . . . . . . 31
Con v ex sets . . . . . . . . . . . . . . . . . . . . . 32
Matrix Theory . . . . . . . . . . . . . . . . . . . . . . . . 38
Eigen v alues and Jordan form . . . . . . . . . . . 39
Self-adjoin t, unitary and p ositiv e de nite matrices 41
Singular v alue p osition . . . . . . . . . . . 45
Linear Matrix Inequalities . . . . . . . . . . . . . . . . . 47
ii Con ten ts
Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2 State Space System Theory 57
The autonomous system . . . . . . . . . . . . . . . . . . 58
Con trollabilit y . . . . . . . . . . . . . . . . . . . . . . . . 61
Reac habilit y . . . .