(→Nonlinear Second-Order System: expand section title) |
(→Affine Parametric Second-Order System: expand section title) |
||
Line 139: | Line 139: | ||
When <math>C_v = 0</math>, we denote <math>C = C_p</math>. |
When <math>C_v = 0</math>, we denote <math>C = C_p</math>. |
||
− | ===Affine Parametric |
+ | ===Affine Parametric LTI-SOS (AP-LTI-SOS)=== |
:<math> |
:<math> |
Revision as of 21:02, 20 April 2023
Benchmark Model Templates
This page specifies templates for the types of models used as benchmark systems. In particular, the naming schemes established here are used in the corresponding data sets for all benchmarks. For example, always serves as the name of the component matrix applied to the state
in a linear time-invariant system.
For all models we assume an input
, with components
,
a state
,
and an output
.
For all parametric models, we assume each component has
parameters; in cases where a component has fewer than
parameters, the extras are treated as
.
Some benchmarks (e.g., Bone Model) have a constant forcing term, in which case, it is assumed that
is identically
.
Linear Time-Invariant First-Order System (LTI-FOS)
with
,
,
,
,
.
Linear Time-Varying First-Order System (LTV-FOS)
with
,
,
,
,
.
Quadratic-Bilinear System (QBS)
with
,
,
,
,
,
,
.
Nonlinear Time-Invariant First-Order System (NLTI-FOS)
with
,
,
,
,
,
.
Affine Parametric LTI-FOS (AP-LTI-FOS)
with
;
;
; and
,
for all
.
Linear Time-Invariant Second-Order System (LTI-SOS)
with
,
,
,
,
,
.
When , we denote
.
Nonlinear Time-Invariant Second-Order System (NLTI-SOS)
with
,
,
,
,
,
,
,
.
When , we denote
.
Affine Parametric LTI-SOS (AP-LTI-SOS)
with
;
;
;
; and
,
for all
.