linear_system.h File Reference

#include <memory>
#include <optional>
#include <utility>
#include <variant>
#include "drake/common/drake_copyable.h"
#include "drake/common/symbolic/expression.h"
#include "drake/systems/primitives/affine_system.h"

Include dependency graph for linear_system.h:

This graph shows which files directly or indirectly include this file:

Classes
class	LinearSystem< T >
	A discrete OR continuous linear system. More...
class	TimeVaryingLinearSystem< T >
	Base class for a discrete or continuous linear time-varying (LTV) system. More...

Namespaces
	drake
	drake::systems

Functions
std::unique_ptr< LinearSystem< double > >	Linearize (const System< double > &system, const Context< double > &context, std::variant< InputPortSelection, InputPortIndex > input_port_index=InputPortSelection::kUseFirstInputIfItExists, std::variant< OutputPortSelection, OutputPortIndex > output_port_index=OutputPortSelection::kUseFirstOutputIfItExists, double equilibrium_check_tolerance=1e-6)
	Takes the first-order Taylor expansion of a System around a nominal operating point (defined by the Context). More...
std::unique_ptr< AffineSystem< double > >	FirstOrderTaylorApproximation (const System< double > &system, const Context< double > &context, std::variant< InputPortSelection, InputPortIndex > input_port_index=InputPortSelection::kUseFirstInputIfItExists, std::variant< OutputPortSelection, OutputPortIndex > output_port_index=OutputPortSelection::kUseFirstOutputIfItExists)
	A first-order Taylor series approximation to a system in the neighborhood of an arbitrary point. More...
Eigen::MatrixXd	ControllabilityMatrix (const LinearSystem< double > &sys)
	Returns the controllability matrix: R = [B, AB, ..., A^{n-1}B]. More...
bool	IsControllable (const LinearSystem< double > &sys, std::optional< double > threshold=std::nullopt)
	Returns true iff the controllability matrix is full row rank. More...
Eigen::MatrixXd	ObservabilityMatrix (const LinearSystem< double > &sys)
	Returns the observability matrix: O = [ C; CA; ...; CA^{n-1} ]. More...
bool	IsObservable (const LinearSystem< double > &sys, std::optional< double > threshold=std::nullopt)
	Returns true iff the observability matrix is full column rank. More...
bool	IsStabilizable (const LinearSystem< double > &sys, std::optional< double > threshold=std::nullopt)
	Returns true iff the system is stabilizable. More...
bool	IsDetectable (const LinearSystem< double > &sys, std::optional< double > threshold=std::nullopt)
	Returns true iff the system is detectable. More...