Other Definitions
proper (dict)

Proper

Proper in control theory

Example

$\backslash textbf\{G\}(s)\; =\; \backslash frac\{\backslash textbf\{N\}(s)\}\{\backslash textbf\{D\}(s)\}\; =\; \backslash frac\{s^\{4\}\; +\; n\_\{1\}s^\{3\}\; +\; n\_\{2\}s^\{2\}\; +\; n\_\{3\}s\; +\; n\_\{4\}\}\{s^\{4\}\; +\; d\_\{1\}s^\{3\}\; +\; d\_\{2\}s^\{2\}\; +\; d\_\{3\}s\; +\; d\_\{4\}\}$

$deg(\backslash textbf\{N\}(s))\; =\; 4\; \backslash leq\; deg(\backslash textbf\{D\}(s))\; =\; 4$.

$\backslash textbf\{G\}(s)\; =\; \backslash frac\{\backslash textbf\{N\}(s)\}\{\backslash textbf\{D\}(s)\}\; =\; \backslash frac\{s^\{4\}\; +\; n\_\{1\}s^\{3\}\; +\; n\_\{2\}s^\{2\}\; +\; n\_\{3\}s\; +\; n\_\{4\}\}\{d\_\{1\}s^\{3\}\; +\; d\_\{2\}s^\{2\}\; +\; d\_\{3\}s\; +\; d\_\{4\}\}$

$deg(\backslash textbf\{N\}(s))\; =\; 4\; \backslash nleq\; deg(\backslash textbf\{D\}(s))\; =\; 3$.

Implications

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