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Or to show how certain control problems can be solved. e. 5) Observe that we do not transform the input and output signals because we want to preserve the input–output behavior of the state representations to have equivalent state-space models. 3 Special Realization Forms of LTI Systems Realizations of special forms play an important role in investigating the dynamic properties of an LTI system. Diagonal Form Realization. Diagonal form realization is characterized by a diagonal state matrix A that plays a role in analyzing asymptotic stability.

Continuous Time and Discrete Time Signals. In systems and control theory, one usually has a one-dimensional independent variable set which is called time and denoted by T in the general case. TLFeBook 10 2. e. T ⊆ R. e. T ⊆ N. Bounded and Unbounded Signals. A signal x : R → C is bounded if |x(t)| is finite for all t. A signal that does not have this property is unbounded. Periodic and Aperiodic Signals. A time-dependent real-valued signal x : R → R is periodic with period T if x(t + T ) = x(t) for all t.

P (output equation) with the same state, input and output vectors x, u and y as above. It is easy to see that bilinear state-space models are special cases of the input-affine models, because the input signal enters into the model in a linear way. 1 that a wide class of process systems models belong to the class of bilinear state-space models. 2 by changing the input variables to have u = [ v c , v h ]T and considering the elements of the old input vector uO = [ uO1 , uO2 ]T = [ TcIN , ThIN ]T to be constants.

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