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信号与系统英文版教学课件：ch8 State Model Representation.ppt

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信号与系统英文版教学课件：ch8 State Model Representation.ppt

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Ch8. State Model Representation



There are two types of mathematical models of

systems: input/output representation and state-

variable representation.



The input/output representation describes the

input/output behavior of systems.



The state-variable representation describes the

internal behavior of systems.



The objective of this chapter: define the state model

and study the basic properties of this model for both

continuous-time and discrete-time systems.

INTRODUCTION

Ch8. State Model Representation

1. State model

For a single-input single-output causal continuous-time

system, its

input : v(t)

output: y(t)

Obviously it is not. The reason is that the application of

the input v(t) for may put energy into the system

that affects the output response for .

tt 

tt 

Consider the question:

At a value t

of the time variable t , is it possible to

compute the output response y(t) from only the

knowledge of the input v(t) for ?

Ch8. State Model Representation



If the system is zero at t

, y(t) can be computed from

v(t) for .

tt 



If the system is not zero at t

, knowledge of the state is

necessary to be able to compute the output y(t).



For any time point t

, the state x(t) of the system at

time is defined to be that portion of the past

history of the system required to determine the

output response y(t) for all

given the input v(t) for

A nonzero state at time indicates the

presence of energy in the system at time .

tt 

 

tt 

tt 

)(

Ch8. State Model Representation

Example 8.1 Consider the circuit in following figure.

compute the currents in L1 and L2, and the voltage

on C.

Let x

be the current in L

be the voltage on C,

222

213

232222

111311

exRy

xxxCKCL

exxRxL

exRxxL

KVL





















Ch8. State Model Representation

Rewrite the former equations, respectively, as

222

213

exRy











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