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Ch 2 Solution of State space Equations

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Engineering/Scientific Theories A model or framework for understanding A set of statements closed under certain rules of inference Validated & tested (not mere conjectures) Summarizes (infinitely) many practical situations –Requires abstraction Types –Categorization (system of naming things) –Summarizes past experiences –Predicts future outcomes –Tool to design with State space theory –super theory (physics, chemistry, etc hence abstract) –Helps understand engineering analysis and design techniques

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CT vs DT Discrete time state equations Continuous time state equations

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Discrete time State Equations Possibly nonlinear, most general, hardest to analyze Linear, possibly time-varying Linear & time-invariant, easiest to analyze, provides most convenient design techniques

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Continuous time State Equations Possibly nonlinear, most general, hardest to analyze Linear, possibly time-varying Linear & time-invariant, easiest to analyze, provides most convenient design techniques

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Solve LTI DT state equations Free response Forced response Weighting sequence (Markov parameters) External equivalence Impulse response Convolution

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Solve LTI CT state equations Scalar equation Vector-matrix equation –Matrix exponential Existence, uniqueness, Lipschitz condition Free response, forced response State transition matrix Linearity Complete response Impulse response convolution

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Discretization

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