Stability Theory of Dynamical Systems

asymp autonomous system bounded c₁ Chapter characteristic multipliers convergence decrescent denote derivative differential equation discrete system dynamic system eigenvalues equilibrium point equivalent exists forced system function V(x G(jw hence Hurwitz impulse response initial input input-output stability Jordan canonical form k₁ lemma Liapunov function limit cycle linear system matrix A(t motion necessary and sufficient negative definite negative real nonlinear system null solution Nyquist criterion Nyquist plot obtained orbital stability origin periodic solution periodic system phase plane Popov criterion positive constant positive real Proof proved quadratic form radially unbounded real axis region root locus Rosenbrock Routh satisfies second-order system Section shown in Fig shows solution of 1.1 solution of system stability criterion stability properties sufficient condition system equation system of Fig system x system X1 t₁ Theorem 4.1 Theory tion transition matrix uniformly asymptotically stable uniformly stable unstable vector x₁ Xk+1 yields λι