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associated asymptotically stable axis basis vectors canonical Chap column vector concepts constant system control system coordinates corresponding defined determinant diagonal matrix difference equations differential equation differential system discrete-time systems discussion eigenvalues eigenvectors elements equilibrium point feedback Find flow diagram flow graph following example geometric illustrated in Fig impulse response initial conditions inner product input Kalman Laplace transform limit cycle linear operator linear space linear systems linearly independent Lyapunov function mathematical matrix exponential method motion n-dimensional node nonlinear nonsingular notation observable origin orthogonal output phase plane polynomial positive definite problem quadratic form rank sampled-data systems sampling scalar solution subspace Suppose system in Prob system of Eq t,to t₁ techniques time-invariant time-varying systems trajectory transfer function transition matrix u₁ V₁ variables vector space x(to x₁ Xk+1 y₁ z transform zero zero-input response λι