Definition of Stability Stability is an important concept in linear systems — we all want to fly in airplanes with stable control systems! Although many of us have an intuitive feel for the idea of “stability,” we need a working definition that will allow us to classify systems as either stable or unstable. Working with a partner, draft a definition of stability. The definition should be specific enough that you can test whether a system with impulse response g(t) (or equivalently, transfer function G(s)) is stable or not. Note: There are dozens, and maybe hundreds, of definitions of stability. There is no “wrong” answer! When you are finished, press “1” on your PRS remote.Definition of Stability Solution Gu(t)y(t)The LTI system G is Bounded Input / Bounded Output (BIBO) stable if every bounded input u(t) produces a bounded output y(t). Basically, this definition says that every “nice” input produces a “nice” output.BIBO Stability I Consider the systems F , G, and H, with impulse responses given by f(t) = σ(t)e−2t g(t) = σ(t) h(t) = σ(t)e t Which of the systems are BIBO stable? 1. F , G, and H 2. F and G 3. F only 4. G and H 5. H only 6. none of the aboveBIBO Stability I Consider the systems F , G, and H, with impulse responses given by f(t) = σ(t)e−2t g(t) = σ(t) h(t) = σ(t)e t Which of the systems are BIBO stable? The correct answer is: 1. F , G, and H 2. F and G 3. ♥ F only 4. G and H 5. H only 6. none of the aboveBIBO Stability II Consider the system G with impulse response given by 1 g(t) = σ(t)1 + t Is the system G BIBO stable? 1. Yes 2. No 3. Don’t knowBIBO Stability II Consider the system G with impulse response given by 1 g(t) = σ(t)1 + t Is the system G BIBO stable? The correct answer is: 1. Yes 2. ♥ No 3. Don’t knowBIBO Stability III Consider the system G with impulse response given by 1 g(t) = σ(t)√t Is the system G BIBO stable? 1. Yes 2. No 3. Don’t knowBIBO Stability III Consider the system G with impulse response given by 1 g(t) = σ(t)√t Is the system G BIBO stable? The correct answer is: 1. Yes 2. ♥ No 3. Don’t
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