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EE200_Weber_9-11

# EE200_Weber_9-11 - EE 200 Infinite State Machines A state...

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1 EE 200 Infinite State Machines A state machine is define by a five-tuple M = (States, Inputs, Outputs, update, initialState) Assumptions: We can have an infinite number of states. The input set, output set and state space are numeric sets so we can work with them mathematically. States, s(n), are N-tuples in Real N Inputs, x(n), are M-tuples in Real M Outputs, y(n), are K-tuples in Real K

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2 EE 200 Infinite State Machines Each state the system can be in is defined by a collection of N real numbers, not a just a single value. Each input to and output from the system are a collection of M or K real numbers. The update function is defined as update: Real N × Real M Real N × Real K Or separately update = (nextState, output) nextState: Real N × Real M Real N output: Real N × Real M Real K
3 EE 200 Infinite State Machines For a input sequence of M-tuples (x(0), x(1), x(2), …) the state update equation n Integers, n 0, s(n+1) = nextState(s(n), x(n)) generates a state response of N-tuples (s(1), s(2), s(3), … ), and an output equation n Integers, n 0, y(n) = output(s(n), x(n)) generates an output response of K-tuples (y(0), y(1), y(2), … ). The state update equation and output equation together are the state-space model of the system.

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4 EE 200 Infinite State Machines The state update and output equations can both be viewed as collections of equations, one for each element of the tuple: nextState(s,x) = (nextState 1 (s,x), … , nextState M (s,x)) output(s,x) = (output 1 (s,x), … , output K (s,x)) where nextState i (s,x): Real N × Real M Real, i = 1, … , M output i (s,x): Real N × Real M Real, i = 1, … , K
5 EE 200 Infinite State Machines

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EE200_Weber_9-11 - EE 200 Infinite State Machines A state...

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