Analyse the stability of the following dynamical systems by using Lyapunov theory. All bold small letters...
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Analyse the stability of the following dynamical systems by using Lyapunov theory. All bold small letters (e.g., v) are assumed to be column vectors. Are these systems stable, asymptotically stable, or unstable? Analytically demonstrate it. 2) y + y = u where the control input is defined as u = - 3) w = -AT Aw -5(y- yd), for yd as a desired constant target where A € Rmxn, for m > n, is a "short and fat" matrix with full-row rank. 4) x = -x³ - (x - x²) where x is a constant scalar. 5) s = ks where k > 0 is a constant scalar. Analyse the stability of the following dynamical systems by using Lyapunov theory. All bold small letters (e.g., v) are assumed to be column vectors. Are these systems stable, asymptotically stable, or unstable? Analytically demonstrate it. 2) y + y = u where the control input is defined as u = - 3) w = -AT Aw -5(y- yd), for yd as a desired constant target where A € Rmxn, for m > n, is a "short and fat" matrix with full-row rank. 4) x = -x³ - (x - x²) where x is a constant scalar. 5) s = ks where k > 0 is a constant scalar.
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Solution 2 The dynamical system is described by the equation y y u where u is the control input To use Lyapunov theory we need to define a Lyapunov fu... View the full answer
Related Book For
Fundamentals of Thermal-Fluid Sciences
ISBN: 978-0078027680
5th edition
Authors: Yunus A. Cengel, Robert H. Turner, John M. Cimbala
Posted Date:
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