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Language notation and basic
Concepts and properties associated
Basic properties of state and state equations
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adders adjoint applied associated assume assumption asymptotically stable basis functions Chap coefficients column complex numbers components concept constant convergence Corollary corresponding defined delta functions denoted derivative determined differential equation differential operator differential operator type eigenvalues eigenvectors elements expression finite given hence identical implies impulse response initial input segment space input-output pair input-output relation input-output-state relation integrators interconnection interval inverse Laplace transform linear combination linear systems linear time-invariant system linear transformation linearly independent minimal polynomial n-tuples node nonsingular notation Note notion object observation obtain orthogonal output polynomial Proof representation represented respectively result satisfies scalar product self-consistency condition shown in Fig signal-flow graph simple solution strictly stable subspace Suppose system characterized terminal variables Theorem Let time-varying tion transfer function transition matrix unique values vector space voltage zero zero-input response zero-state equivalent zero-state linear zero-state response