Summary
This chapter illustrates various finite-time analysis and design problems for linear systems. Most of this work deals with continuous-time systems. First, some conditions for finite-time stability and boundedness are presented; then we turn to the design problem. In this context, we consider both the state feedback and the output feedback synthesis. For both cases, we end up with some sufficient conditions involving linear matrix inequalities (both algebraic and differential). The last section of the chapter extends the previous results to discrete-time systems.
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References
Abdallah CT, Amato F, Ariola M, Dorato P, Koltchinski V (2002) Statistical learning methods in linear algebra and control problems: the example of finite-time control of uncertain linear systems. Linear Algebra and its Applications 351–352: 11–26
Amato F, Ariola M, Cosentino C (2003a) Finite-time control with pole placement. Proc. of the 2003 European Control Conference, Cambridge
Amato F, Ariola M, Cosentino C (2003b) Robust finite-time stabilization via dynamic output feedback: an LMI approach. Proc. of IFAC ROCOND 2003, Milan
Amato F, Ariola M, Cosentino C (2005) Finite-time control of linear time-varying systems via output feedback. Submitted
Amato F, Ariola M, Cosentino C, Abdallah C, Dorato P (2003) Necessary and sufficient conditions for finite-time stability of linear systems. Proc. of the 2003 American Control Conference, Denver, CO, 4452–4456
Amato F, Ariola M, Cosentino C, Carbone M (2004a) Finite-time stability of discrete-time systems. Proc. of the 2004 American Control Conference, Boston, MA, 1440–1444
Amato F, Ariola M, Cosentino C, Carbone M (2004b) Finite-time output feedback control of discrete-time systems. Submitted
Amato F, Ariola M, Dorato P (2001) Finite-time control of linear systems subject to parametric uncertainities and disturbances. Automatica 37:1459–1463
Bernussou J, Peres PLD, Geromel JC (1989) A linear programming oriented procedure for quadratic stabilization of uncertain systems. Systems & Control Letters 13:65–72
Boyd S, El Ghaoui L, Feron E, Balakrishnan V (1994) Linear matrix inequalities in system and control theory. SIAM, Philadelphia, PA
D’Angelo H (1970) Linear time-varying systems: analysis and synthesis. Allyn and Bacon, Boston, MA
Dorato P (1961) Short time stability in linear time-varying systems. Proc. IRE International Convention Record Part 4, 83–87
Gahinet P (1996) Explicit controller formulas for LMI-based H ∞ synthesis. Automatica 32:1007–1014
Weiss L, Infante EF (1967) Finite time stability under perturbing forces and on product spaces. IEEE Transactions Automatic Control 12:54–59
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Amato, F., Ariola, M., Carbone, M., Cosentino, C. (2006). Finite-Time Control of Linear Systems: A Survey. In: Menini, L., Zaccarian, L., Abdallah, C.T. (eds) Current Trends in Nonlinear Systems and Control. Systems and Control: Foundations & Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4470-9_11
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DOI: https://doi.org/10.1007/0-8176-4470-9_11
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