cited from [https://ccrma.stanford.edu/~jos/fp/State_Space_Realization.html]
IIR filters have an extensively used matrix representation called state space form (or ``state space realizations''). They are especially convenient for representing filters with multiple inputs andmultiple outputs (MIMO filters). An order 
digital filter with 
inputs and 
outputs can be written in state-space form as follows:
where
is the length state vector at discrete time 
, 
is a 
vector of inputs, and 
the 
output vector. 
is the 
state transition matrix, and it determines thedynamics of the system (its poles, or resonant modes).
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