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Transfer Functions and Block Diagrams
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adjoint variables assumed asymptotically stable augmented functional bang-bang control block diagram CHAPTER characteristic equation characteristic polynomial closed loop system coefficients companion form consider constant constraint contour control theory controllable and observable corresponding criterion damping determined diagonal form dynamic economic rent eigenvalues Eliminating end point equilibrium Euler equation example extremum values follows form the augmented frequency given gives Hamiltonian Hence illustrated in Fig initial conditions input integral Lagrange multiplier linear systems mathematical maximise method minimise minimum modes non-singular non-singular matrix Nyquist obtain optimal control optimal path optimal trajectory output polynomial Pontryagin's Minimum Principle positive response result roots s-plane shown in Fig solution solve specified Stage State Action state-space switching curve Sylvester's criterion system defined system is controllable system is stable theorem transfer function G(s transversality condition uncontrollable units of milk unobservable unstable vector zero