Converting Differential to Difference Equation

Calculus Level pending

The reader is asked to refer to the following note to solve this very easy problem. The boxed equations in the note will directly lead to the answer.

Conversion of Differential Equation to Difference Equation

Consider the differential equation: x ˙ = x + u \dot{x} = x + u

Here, x = x ( t ) x=x(t) represents a time-dependent quantity of the system whereas u = u ( t ) u = u(t) is a general time-varying function. This equation is converted to a difference equation of the form:

x ( T + h ) = a x ( T ) + b u ( T ) x(T+h) = a x(T) + b u(T)

Where T T is an arbitrary time instant and h = 0.1 h = 0.1 s. Also, a a and b b are real numbers. Compute:

1000 ( a + b ) \lfloor 1000(a+b) \rfloor

Note: . \lfloor . \rfloor denotes the floor function.


The answer is 1210.

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