# lect1 - EL 625 Lecture 1 1 EL 625 Lecture 1 Denition A...

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EL 625 Lecture 1 1 EL 625 Lecture 1 Definition : A physical system is an interconnection of physical components that perform a specific function. These components may be electrical, mechanical,hydraulic,thermal and so forth. System S - u 1 - u 2 - u r - y 1 - y 2 - y m Inputs or excitations Outputs or responses Inputs : signals that can be directly changed with time in order to effect indirectly desired changes in some other signals of the system which are of particular interest (which are called out- puts ) Using vector notation,

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EL 625 Lecture 1 2 u ( t ) = u 1 ( t ) u 2 ( t ) u 3 ( t ) . . . u r ( t ) y ( t ) = y 1 ( t ) y 2 ( t ) y 3 ( t ) . . . y m ( t ) System S - u ( t ) - y ( t ) y ( t ) = S { u ( t ) } ‘Input-output relation’ y e = S { u e } y e and u e represent the entire time functions y and u respectively.
EL 625 Lecture 1 3 Classification of Systems Type of system Brief Description Dynamic system has memory; output at time t de- pends on inputs at times other than t Static System has no memory (zero memory) ; output at time t depends on input only at time t MIMO Multi-Input-Multi-Output - many inputs and outputs SISO Single-Input-Single-Output - one input and one output Continuous-time differential equations Discrete-time difference equations Causal System is not predictive - output depends only on past values of input Non-causal output depends on future values of input also Linear Superposition holds Non-linear ‘not linear’ - Superposition does not hold

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EL 625 Lecture 1 4 Finite-Dimensional finite number of states required to charac- terize the system - ‘lumped’ system Infinite-Dimensional
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