Static and dynamic System:

Static system:-

 A static system is a system which output at any instant of time depends on the input sample at the same time. In other word, the system in which output depends only on the present input at any instant of time then the system is known as static system. This system also know as memoryless system.

 Consider a system in which x(t) is the input and y(t) is the output of that system.

Examples:-

1. If y(t) = 2 x(t)

    

   Put t = 0, y(0) = 2 x(0)

   Put t = 1, y(1) = 2 x(1)

   Put t = 2, y(2) = 2 x(2)

   Put t = 3, y(3) = 2 x(3)

2. If y(t) = x²(t)

   Put t = 1,  y(1) = x²(1)

   Put t = 2,  y(2) = x²(2)

   Put t = -1, y(-1) = x²(-1)

   Put t = -2, y(-2) = x²(-2)

 In the above examples, the output y(t) at ‘t' instant depends on the input x(t) at the same time instant ‘t' (present time). So this system is static system.

Dynamic System:-

 A dynamic system is a system in which output at any instant of time depends on the input sample at the same time as well as at other times(future and/or past inputs). In other words, the system in which output depends on the past and/or future input at any instant of time then this system is known as the dynamic system. This system also known as the possesses memory system. 

 Consider a system in which x(t) is the input and y(t) is the output of that system.

Examples:-

1. If y(t) = 2 x(t) − 3 x(t−1)

    

   put t = 0, y(0) = 2 x(0) − 3 x(−1)

   put t = −2, y(−2) = 2 x(−2) − 3 x(−3)

2. If y(t) = − 3 x(−t)

    put t = 0, y(1) = − 3 x(0)

    put t = 1, y(1) = − 3 x(−1)

    put t = −2, y(−2) = − 3 x(2)

 In the above example, the output y(t) depends on present input, past input and future input. So this system is a dynamic system.