ABSTRACT
The dynamical systems theory and the control theory have been mainly developed for the linear Input‐State‐Output (ISO) (dynamical, control) systems . Their mathematical models contain the state vector differential equation (3.1) and the output algebraic vector equation (3.2), d X ( t ) dt = A X ( t ) + D D ( t ) + B U ( t ) = A X ( t ) + P I ( t ) , ∀ t ∈ T 0 , A ∈ ℜ n × n , D ∈ ℜ n × d , B ∈ ℜ n × r , P = [ D ⋮ B ] ∈ ℜ n × ( d + r ) , $$ \begin{gathered} \frac{{dX(t)}}{{dt}} = AX(t) + DD(t) + BU(t) = AX(t) + PI(t)~,~\forall t \in {\mathfrak{T}}_{0} , \hfill \\ A \in {\Re }^{{n \times n}} ,D \in {\Re }^{{n \times d}} ,B \in {\Re }^{{n \times r}} ,P = [D~ \vdots ~B] \in {\Re }^{{n \times (d + r)}} , \hfill \\ \end{gathered} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432149/418cc552-67ff-4e7e-a408-87b73829f6e7/content/math3_1.tif"/> Y ( t ) = C X ( t ) + V D ( t ) + U U ( t ) = C X ( t ) + Q I ( t ) , ∀ t ∈ T 0 , C ∈ ℜ N × n , V ∈ ℜ N × d , U ∈ ℜ N × r , Q = [ V ⋮ U ] ∈ ℜ N × ( d + r ) . $$ \begin{gathered} Y(t) = CX(t) + VD(t) + U{\text{U}}(t) = CX(t) + QI(t)~,~\forall t \in {\mathfrak{T}}_{0} , \hfill \\ C \in {\Re }^{{N \times n}} ,V \in {\Re }^{{N \times d}} ,U \in {\Re }^{{N \times r}} ,Q = [V~ \vdots ~U] \in {\Re }^{{N \times (d + r)}} . \hfill \\ \end{gathered} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429432149/418cc552-67ff-4e7e-a408-87b73829f6e7/content/math3_2.tif"/>
