ABSTRACT
This chapter defines the tensor product (TP) type model representation of quasilinear parameter-varying (qLPV) state space models. Consider the following state space model:
x˙(t) = A(p(t))x(t) + B(p(t))u(t) y(t) = C(p(t))x(t) + D(p(t))u(t) , (2.1)
with input u(t) ∈ Rk, output y(t) ∈ Rl, and state vector x(t) ∈ Rm. The system matrix
S(p(t)) = ( A(p(t)) B(p(t)) C(p(t)) D(p(t))
) ∈ R(m+k)×(m+l) (2.2)
is a parameter-varying quantity, where p(t) ∈ Ω is a time-varying N-dimensional parameter vector within the closed hypercube Ω = [a1, b1] × [a2, b2] × · · · × [aN , bN] ⊂ RN . If the parameter p(t) does not include any element of x(t), (2.1) is a linear parameter-varying (LPV) system. If the parameter p(t) does include some elements of x(t), system (2.1) then belongs to the class of nonlinear models. In this case, it is termed a qLPV model.
