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Stabilization and Control of Fractional Order Systems: A Sliding Mode Approach
Calculus thrives on continuity. At its core is the assumption that things change smoothly,
that everything is only infinitesimally different from what it was a moment before. Like a
movie, calculus reimagines reality as a series of snapshots, and then recombines them,
instant by instant, frame by frame, the succession of imperceptible changes creating an
illusion of seamless flow. This way of understanding a change has proven to be powerful
beyond words, perhaps the greatest idea that humanity has ever had.
Yet in another way, calculus is fundamentally naive, almost childish in its optimism.
Experience teaches us that change can be sudden, discontinuous, and wrenching. Calculus
draws its power by refusing to see that. It insists on a world without accidents, where one
thing leads logically to another. Give me the initial conditions and the law of motion, and
with calculus I can predict the future or better yet, reconstruct the past.
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