# Ch 2 Solution of State space Equations - PowerPoint PPT Presentation

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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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## 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

• 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

### CT vs DT

• Discrete time state equations

• Continuous time state equations

### 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

### 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

### Solve LTI DT state equations

• Free response

• Forced response

• Weighting sequence (Markov parameters)

• External equivalence

• Impulse response

• Convolution

### 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