Linear System TheoryAn introduction to linear system theory which focuses on time-varying linear systems, with frequent specialization to time-invariant case. The text is modular for flexibility and provides compact treatments of esoteric topics such as the polynomial fraction description and the geometric theory. |
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Contents
MATHEMATICAL NOTATION AND REVIEW | 1 |
Linear Quadratic Methods | 17 |
STATE EQUATION REPRESENTATION | 19 |
Copyright | |
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Automatic Control Chapter characteristic polynomial closed-loop state equation coefficient matrices column compute controllability and observability controllability subspace controlled invariant subspace convergence coprime corresponding defined diagonal differential equation eigenvalues entries equation x(t Example Exercise given IEEE Transactions implies impulse response input signal integral invariant subspace contained invertible Laplace transform Lemma linear state equation linearly independent matrix exponential minimal realization n x 1 vector n x n matrix noninteracting control nonzero notation Note polynomial fraction description polynomial matrix positive constant positive semidefinite proof of Theorem properties rank right polynomial fraction satisfies scalar sequence solution spectral norm symmetric matrix T-periodic t₁ Theorem Suppose time-invariant linear time-varying time-varying systems tion Transactions on Automatic transfer function transition matrix uniform exponential stability uniformly bounded-input uniformly exponentially stable uniformly stable unimodular variable change weighting pattern zero zero-state response ㅁㅁㅁ