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## ISSN 0280–5316 ISRN LUTFD2/TFRT--7582--SE PWLT L A Matlab toolbox for analysis of Piecewise Linear Systems (1999)

### Citations

1600 |
Fuzzy identification of systems and its applications to modeling and control,”
- Takagi, Sugeno
- 1985
(Show Context)
Citation Context ... nonlinear systems, the toolbox allows the system dynamics to lie in the convex hull of a set of piecewise affine systems, see [5]. This is e.g. useful for the analysis of fuzzy Takagi-Sugeno systems =-=[8]-=-. For convenient notation, we introduce Āi � � � Ai ai 0 0 � � x ¯Ci �[Ci ci] ¯x� 1 A large part of the analysis results will be concerned with (global) properties of equilibria. We therefore let I0 ⊆... |

245 | Computation of piecewise quadratic Lyapunov functions for hybrid systems,”
- Johansson, Rantzer
- 1998
(Show Context)
Citation Context ...the index set of the cells. In order to allow rigorous analysis of smooth nonlinear systems, the toolbox allows the system dynamics to lie in the convex hull of a set of piecewise affine systems, see =-=[5]-=-. This is e.g. useful for the analysis of fuzzy Takagi-Sugeno systems [8]. For convenient notation, we introduce Āi � � � Ai ai 0 0 � � x ¯Ci �[Ci ci] ¯x� 1 A large part of the analysis results will b... |

95 | Piecewise linear quadratic optimal control.
- Rantzer, Johansson
- 2000
(Show Context)
Citation Context ...piecewise linear systems. The simulation routines detect sliding modes and simulate equivalent dynamics [2]. The analysis and design are based on computation of piecewise quadratic Lyapunov functions =-=[6]-=-. The computations are performed using convex optimization in terms of linear matrix inequalities (LMIs). This version of the toolbox requires the LMI control toolbox [1]. The structure of this manual... |

94 |
Piecewise Linear Control Systems
- Johansson
- 2003
(Show Context)
Citation Context ...onsequently, the simulation of a PWL system does not require these matrices. Also note that Eq. (3) does not uniqely define the F-matrices. A more detailed description of the matrices can be found in =-=[4]-=-. For the inexperienced user, who might find it difficult to create appropriate F-matrices, Section 3 presents means to overcome this problem. 1 The computations in [3, 7] use an additional matrix Ei.... |

7 | A toolbox for computational analysis of piecewise linear systems
- Hedlund, Johansson
- 1999
(Show Context)
Citation Context ...ystems. Key features of the toolbox are modeling, simulation, analysis, and optimal control for piecewise linear systems. The simulation routines detect sliding modes and simulate equivalent dynamics =-=[2]-=-. The analysis and design are based on computation of piecewise quadratic Lyapunov functions [6]. The computations are performed using convex optimization in terms of linear matrix inequalities (LMIs)... |

3 |
LMI Control Toolbox User’s Guide
- Gahine, Nemirovski, et al.
- 1995
(Show Context)
Citation Context ... quadratic Lyapunov functions [6]. The computations are performed using convex optimization in terms of linear matrix inequalities (LMIs). This version of the toolbox requires the LMI control toolbox =-=[1]-=-. The structure of this manual is as follows. Section 2 describes the model representation, i.e. how a piecewise linear (PWL) system is defined in this toolbox. Certain structures of the PWL systems a... |

3 | Global analysis of third-order relay feedback systems
- JOHANSSON, RANTZER
- 1996
(Show Context)
Citation Context ...of the matrices can be found in [4]. For the inexperienced user, who might find it difficult to create appropriate F-matrices, Section 3 presents means to overcome this problem. 1 The computations in =-=[3, 7]-=- use an additional matrix Ei. This matrix is derived directly from the corresponding Gi-matrix, and is therefore not requested from the user. 2sa) b) x2 x1 Figure 2 The special structures that are sup... |