Abstract
This chapter considers the development of conventional sliding mode methods. The chapter describes the early work to define the notion of the solution of differential equations with discontinuous right-hand sides and the concept of “equivalent control” as a means to describe the reduced-order dynamics while a sliding motion is taking place. The main focus of the chapter is on the development of sliding mode design techniques for uncertain linear systems—specifically systems which can be thought of as predominantly linear in a characteristic, or nonlinear systems which can be modeled well (at least locally) by a linear system. For such systems, sliding surfaces formed from linear combinations of the states are considered (i.e., hyperplanes in the state space).
Keywords
- Slide Mode Control
- Switching Function
- Symmetric Positive Definite Matrix
- Equivalent Control
- Regular Form
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- 1.
For details see [158].
- 2.
For details see [158].
- 3.
For details of QR factorization methods see [177].
- 4.
See for example [47].
- 5.
- 6.
A more detailed description of this approach is given in Sect. 4.2.2 in [67] and details about LQR methods appear in Appendix C.
- 7.
Taken from [86].
- 8.
For details see Sect. 4.4.2 in [67] and Appendix C.
- 9.
This situation is discussed further in “Notes and References” in Chap. 8.
- 10.
See “Notes and References” at the end of the chapter.
- 11.
For details and definitions see [175]. This is also discussed in Appendix B.
- 12.
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Shtessel, Y., Edwards, C., Fridman, L., Levant, A. (2014). Conventional Sliding Modes. In: Sliding Mode Control and Observation. Control Engineering. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4893-0_2
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