EECS20N: Signals and Systems


Given the current state s(n) in Reals N and the current input x(n) in Reals M the next state is given by

s(n + 1) = nextState (s(n), x(n))

and the output y(n) in Reals K is given by

y(n) = output (s(n), x(n))

Together, these two equations are called the state-space model of the system. Given an input signal x(0), x(1), x(2), ..., the resulting state trajectory and output signal are obtained recursively:

s(0) = initialState

and for all n Naturals0 ,

s(n +1) = nextState(s(n), x(n)),

y(n) = output(s(n), x(n)).