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Ch 2 Solution of State space Equations

Ch 2 Solution of State space Equations. 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

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Ch 2 Solution of State space Equations

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  1. Ch 2 Solution of State space Equations

  2. 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

  3. CT vs DT • Discrete time state equations • Continuous time state equations

  4. 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

  5. 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

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

  7. 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

  8. Discretization

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