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2014 | OriginalPaper | Chapter

5. Control Design for TDSs

Author : Emilia Fridman

Published in: Introduction to Time-Delay Systems

Publisher: Springer International Publishing

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Abstract

In Chaps. 3 and 4 we have considered Lyapunov-based stability and performance analysis. In this chapter we study design problems. Section 5.1 below gives an idea of a classical predictor-based design and a Linear Quadratic Regulator (LQR) for LTI systems. The infinite horizon LQR design is confined to known and constant system matrices and delays. The next sections of the chapter present robust control via LMIs that leads to efficient design algorithms for linear uncertain systems with constant or time-varying (either known or unknown) intput/output/state delays.

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Literature
9.
go back to reference Bekiaris-Liberis N, Krstic M (2013) Compensation of state-dependent input delay for nonlinear systems. IEEE Trans Automat Control 58(2):275–289MathSciNetCrossRefMATH Bekiaris-Liberis N, Krstic M (2013) Compensation of state-dependent input delay for nonlinear systems. IEEE Trans Automat Control 58(2):275–289MathSciNetCrossRefMATH
10.
go back to reference Bekiaris-Liberis N, Krstic M (2013) Nonlinear control under nonconstant delays, vol 25. SIAM, PhiladelphiaCrossRefMATH Bekiaris-Liberis N, Krstic M (2013) Nonlinear control under nonconstant delays, vol 25. SIAM, PhiladelphiaCrossRefMATH
12.
go back to reference Bensoussan A, Da Prato G, Delfour M, Mitter S (1993) Representation and control of infinite dimensional systems. Systems and control, vol 2. Birkhäuser, Boston Bensoussan A, Da Prato G, Delfour M, Mitter S (1993) Representation and control of infinite dimensional systems. Systems and control, vol 2. Birkhäuser, Boston
13.
go back to reference Bernstein DS, Michel AN (1995) Special issue on saturating actuators. Int J Robust Nonlinear Control 5:375–540CrossRefMATH Bernstein DS, Michel AN (1995) Special issue on saturating actuators. Int J Robust Nonlinear Control 5:375–540CrossRefMATH
30.
go back to reference Crocco L (1951) Aspects of combustion stability in liquid propellant rocket motors, part I: fundamentals - low frequency instability with monopropellants. J Am Rocket Soc 21:163–178CrossRef Crocco L (1951) Aspects of combustion stability in liquid propellant rocket motors, part I: fundamentals - low frequency instability with monopropellants. J Am Rocket Soc 21:163–178CrossRef
32.
go back to reference Curtain R, Zwart H (1995) An introduction to infinite-dimensional linear systems theory, vol 21. Springer, BerlinMATH Curtain R, Zwart H (1995) An introduction to infinite-dimensional linear systems theory, vol 21. Springer, BerlinMATH
35.
go back to reference Dambrine M, Richard J, Borne P (1995) Feedback control of time-delay systems with bounded control and state. Math Probl Eng 1(1):77–87CrossRefMATH Dambrine M, Richard J, Borne P (1995) Feedback control of time-delay systems with bounded control and state. Math Probl Eng 1(1):77–87CrossRefMATH
39.
go back to reference Delfour MC (1986) The linear-quadratic optimal control problem with delays in state and control variables: a state space approach. SIAM J Control Optim 24(5):835–883MathSciNetCrossRefMATH Delfour MC (1986) The linear-quadratic optimal control problem with delays in state and control variables: a state space approach. SIAM J Control Optim 24(5):835–883MathSciNetCrossRefMATH
46.
go back to reference Fiagbedzi Y, Pearson A (1986) Feedback stabilization of linear autonomous time lag systems. IEEE Trans Automat Control 31(9):847–855MathSciNetCrossRefMATH Fiagbedzi Y, Pearson A (1986) Feedback stabilization of linear autonomous time lag systems. IEEE Trans Automat Control 31(9):847–855MathSciNetCrossRefMATH
47.
go back to reference Fiagbedzi Y, Pearson A (1987) A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica 23:311–326MathSciNetCrossRefMATH Fiagbedzi Y, Pearson A (1987) A multistage reduction technique for feedback stabilizing distributed time-lag systems. Automatica 23:311–326MathSciNetCrossRefMATH
49.
go back to reference Fiter C, Fridman E (2013) Stability of piecewise affine systems with state-dependent delay, and application to congestion control. In: 52nd IEEE conference on decision and control Fiter C, Fridman E (2013) Stability of piecewise affine systems with state-dependent delay, and application to congestion control. In: 52nd IEEE conference on decision and control
55.
go back to reference Fridman E (2006) Descriptor discretized Lyapunov functional method: analysis and design. IEEE Trans Automat Control 51:890–896MathSciNetCrossRef Fridman E (2006) Descriptor discretized Lyapunov functional method: analysis and design. IEEE Trans Automat Control 51:890–896MathSciNetCrossRef
65.
go back to reference Fridman E, Shaked U (1998) H ∞ -state-feedback control of linear systems with small state delay. Syst Control Lett 33(3):141–150MathSciNetCrossRefMATH Fridman E, Shaked U (1998) H -state-feedback control of linear systems with small state delay. Syst Control Lett 33(3):141–150MathSciNetCrossRefMATH
66.
68.
go back to reference Fridman E, Shaked U (2001) A new H ∞ filter design for linear time-delay systems. IEEE Trans Signal Process 49(11):2839–2843MathSciNetCrossRef Fridman E, Shaked U (2001) A new H filter design for linear time-delay systems. IEEE Trans Signal Process 49(11):2839–2843MathSciNetCrossRef
75.
go back to reference Fridman E, Tsodik G (2009) H ∞ control of distributed and discrete delay systems via discretized Lyapunov functional. Eur J Control 15(1):84–96MathSciNetCrossRefMATH Fridman E, Tsodik G (2009) H control of distributed and discrete delay systems via discretized Lyapunov functional. Eur J Control 15(1):84–96MathSciNetCrossRefMATH
76.
go back to reference Fridman E, Seuret A, Richard JP (2004) Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8):1441–1446MathSciNetCrossRefMATH Fridman E, Seuret A, Richard JP (2004) Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40(8):1441–1446MathSciNetCrossRefMATH
85.
go back to reference Gershon E, Shaked U (2013) Advanced topics in control and estimation of state-multiplicative noisy systems. Springer, BerlinCrossRefMATH Gershon E, Shaked U (2013) Advanced topics in control and estimation of state-multiplicative noisy systems. Springer, BerlinCrossRefMATH
89.
go back to reference da Silva J, Tarbouriech S (2005) Antiwindup design with guaranteed regions of stability: an LMI-based approach. IEEE Trans Automat Control 50:106–111MathSciNetCrossRef da Silva J, Tarbouriech S (2005) Antiwindup design with guaranteed regions of stability: an LMI-based approach. IEEE Trans Automat Control 50:106–111MathSciNetCrossRef
93.
go back to reference Gouaisbaut F, Dambrine M, Richard JP (2002) Robust control of delay systems: a sliding mode control design via LMI. Syst Control Lett 46:219–230MathSciNetCrossRefMATH Gouaisbaut F, Dambrine M, Richard JP (2002) Robust control of delay systems: a sliding mode control design via LMI. Syst Control Lett 46:219–230MathSciNetCrossRefMATH
98.
100.
109.
go back to reference Han X, Fridman E, Spurgeon S (2012) Sliding mode control in the presence of input delay: a singular perturbation approach. Automatica 48(8):1904–1912MathSciNetCrossRefMATH Han X, Fridman E, Spurgeon S (2012) Sliding mode control in the presence of input delay: a singular perturbation approach. Automatica 48(8):1904–1912MathSciNetCrossRefMATH
111.
go back to reference Hartung F, Krisztin T, Walther H, Wu J (2006) Functional differential equations with state-dependent delays: theory and applications. In: Handbook of differential equations: ordinary differential equations, vol 3, pp 435–545, Elsevier Hartung F, Krisztin T, Walther H, Wu J (2006) Functional differential equations with state-dependent delays: theory and applications. In: Handbook of differential equations: ordinary differential equations, vol 3, pp 435–545, Elsevier
119.
go back to reference Hollot CV, Misra V, Towsley D, Gong W (2002) Analysis and design of controllers for AQM routers supporting TCP flows. IEEE Trans Automat Control 47:945–959MathSciNetCrossRef Hollot CV, Misra V, Towsley D, Gong W (2002) Analysis and design of controllers for AQM routers supporting TCP flows. IEEE Trans Automat Control 47:945–959MathSciNetCrossRef
120.
go back to reference Hu T, Lin Z (2001) Control systems with actuator saturation: analysis and design. Birkhauser, BostonCrossRefMATH Hu T, Lin Z (2001) Control systems with actuator saturation: analysis and design. Birkhauser, BostonCrossRefMATH
135.
go back to reference Kolmanovskii V, Myshkis A (1999) Applied theory of functional differential equations. Kluwer, DordrechtMATH Kolmanovskii V, Myshkis A (1999) Applied theory of functional differential equations. Kluwer, DordrechtMATH
137.
go back to reference Kolmanovskii VB, Shaikhet LE (1996) Control of systems with aftereffect, vol 157. AMS Bookstore, Providence Kolmanovskii VB, Shaikhet LE (1996) Control of systems with aftereffect, vol 157. AMS Bookstore, Providence
139.
go back to reference Krasovskii N (1962) On the analytic construction of an optimal control in a system with time lags. J Appl Math Mech 26(1):50–67MathSciNetCrossRef Krasovskii N (1962) On the analytic construction of an optimal control in a system with time lags. J Appl Math Mech 26(1):50–67MathSciNetCrossRef
140.
go back to reference Krstic M (2009) Delay compensation for nonlinear, adaptive, and PDE systems. Birkhauser, BostonCrossRefMATH Krstic M (2009) Delay compensation for nonlinear, adaptive, and PDE systems. Birkhauser, BostonCrossRefMATH
141.
go back to reference Krstic M (2010) Lyapunov stability of linear predictor feedback for time-varying input delay. IEEE Trans Automat Control 55:554–559MathSciNetCrossRef Krstic M (2010) Lyapunov stability of linear predictor feedback for time-varying input delay. IEEE Trans Automat Control 55:554–559MathSciNetCrossRef
143.
go back to reference Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley, LondonMATH Kwakernaak H, Sivan R (1972) Linear optimal control systems. Wiley, LondonMATH
144.
157.
go back to reference Liu S, Basar T, Srikant R (2005) Pitfalls in the fluid modeling of RTT variations in window-based congestion control. In: Proceedings of INFOCOM, Miami Liu S, Basar T, Srikant R (2005) Pitfalls in the fluid modeling of RTT variations in window-based congestion control. In: Proceedings of INFOCOM, Miami
161.
169.
go back to reference Molchanov A, Pyatnitskii E (1989) Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Syst Control Lett 13:59–64MathSciNetCrossRefMATH Molchanov A, Pyatnitskii E (1989) Criteria of asymptotic stability of differential and difference inclusions encountered in control theory. Syst Control Lett 13:59–64MathSciNetCrossRefMATH
172.
go back to reference Mondié S, Michiels W (2003) Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Trans Automat Control 48(12):2207–2212MathSciNetCrossRef Mondié S, Michiels W (2003) Finite spectrum assignment of unstable time-delay systems with a safe implementation. IEEE Trans Automat Control 48(12):2207–2212MathSciNetCrossRef
173.
go back to reference Moon YS, Park P, Kwon WH, Lee YS (2001) Delay-dependent robust stabilization of uncertain state-delayed systems. Int J Control 74:1447–1455MathSciNetCrossRefMATH Moon YS, Park P, Kwon WH, Lee YS (2001) Delay-dependent robust stabilization of uncertain state-delayed systems. Int J Control 74:1447–1455MathSciNetCrossRefMATH
174.
go back to reference Moon YS, Park PG, Kwon WH (2001) Robust stabilization of uncertain input-delayed systems using reduction method. Automatica 37(2):307–312MathSciNetCrossRefMATH Moon YS, Park PG, Kwon WH (2001) Robust stabilization of uncertain input-delayed systems using reduction method. Automatica 37(2):307–312MathSciNetCrossRefMATH
193.
go back to reference Polyakov A, Efimov D, Perruquetti W, Richard JP (2013) Output stabilization of time-varying input delay systems using interval observation technique. Automatica 49(11):3402–3410MathSciNetCrossRefMATH Polyakov A, Efimov D, Perruquetti W, Richard JP (2013) Output stabilization of time-varying input delay systems using interval observation technique. Automatica 49(11):3402–3410MathSciNetCrossRefMATH
199.
go back to reference Ross D, Flugge-Lotz I (1969) An optimal control problem for systems with differential-difference equation dynamics. SIAM J Control 7:608–623MathSciNetCrossRefMATH Ross D, Flugge-Lotz I (1969) An optimal control problem for systems with differential-difference equation dynamics. SIAM J Control 7:608–623MathSciNetCrossRefMATH
200.
go back to reference Saberi A, Stoorvogel AA (1999) Special issue on control problems with constraints. Int J Robust Nonlinear Control 9(10):583–584CrossRefMATH Saberi A, Stoorvogel AA (1999) Special issue on control problems with constraints. Int J Robust Nonlinear Control 9(10):583–584CrossRefMATH
201.
205.
go back to reference Seuret A, da Silva JG (2012) Taking into account period variations and actuators saturation in sampled-data systems. Syst Control Lett 61:1–10MathSciNetCrossRefMATH Seuret A, da Silva JG (2012) Taking into account period variations and actuators saturation in sampled-data systems. Syst Control Lett 61:1–10MathSciNetCrossRefMATH
211.
go back to reference Smith O (1959) A controller to overcome dead time. ISA 6(2):28–33 Smith O (1959) A controller to overcome dead time. ISA 6(2):28–33
218.
go back to reference Suplin V, Fridman E, Shaked U (2006) H ∞ control of linear uncertain time-delay systems - a projection approach. IEEE Trans Automat Control 51(4):680–685MathSciNetCrossRef Suplin V, Fridman E, Shaked U (2006) H control of linear uncertain time-delay systems - a projection approach. IEEE Trans Automat Control 51(4):680–685MathSciNetCrossRef
219.
go back to reference Suplin V, Fridman E, Shaked U (2007) Sampled-data H ∞ control and filtering: nonuniform uncertain sampling. Automatica 43:1072–1083MathSciNetCrossRefMATH Suplin V, Fridman E, Shaked U (2007) Sampled-data H control and filtering: nonuniform uncertain sampling. Automatica 43:1072–1083MathSciNetCrossRefMATH
222.
go back to reference Tarbouriech S, da Silva JG (2000) Synthesis of controllers for continuous-time delay systems with saturating controls via LMI’s. IEEE Trans Automat Control 45:105–111MathSciNetCrossRefMATH Tarbouriech S, da Silva JG (2000) Synthesis of controllers for continuous-time delay systems with saturating controls via LMI’s. IEEE Trans Automat Control 45:105–111MathSciNetCrossRefMATH
225.
go back to reference Uchida K, Shimemura E, Kubo T, Abe N (1988) The linear-quadratic optimal control approach to feedback control design for systems with delay. Automatica 24(6):773–780MathSciNetCrossRefMATH Uchida K, Shimemura E, Kubo T, Abe N (1988) The linear-quadratic optimal control approach to feedback control design for systems with delay. Automatica 24(6):773–780MathSciNetCrossRefMATH
230.
go back to reference Vinter R, Kwong R (1981) The infinite time quadratic control problem for linear systems with state and control delays: an evolution equation approach. SIAM J Control Optim 19(1):139–153MathSciNetCrossRefMATH Vinter R, Kwong R (1981) The infinite time quadratic control problem for linear systems with state and control delays: an evolution equation approach. SIAM J Control Optim 19(1):139–153MathSciNetCrossRefMATH
234.
go back to reference Witrant E, Georges D, de Wit CC, Alamir M (2007) On the use of state predictors in networked control systems. In: Chiasson J, Loiseau JJ (eds) Applications of time-delay systems. Springer, Berlin, pp 315–327 Witrant E, Georges D, de Wit CC, Alamir M (2007) On the use of state predictors in networked control systems. In: Chiasson J, Loiseau JJ (eds) Applications of time-delay systems. Springer, Berlin, pp 315–327
235.
go back to reference Wu M, He Y, She JH (2010) Stability analysis and robust control of time-delay systems. Science Press/Springer, Beijing/BerlinCrossRefMATH Wu M, He Y, She JH (2010) Stability analysis and robust control of time-delay systems. Science Press/Springer, Beijing/BerlinCrossRefMATH
237.
go back to reference Xie L, Fridman E, Shaked U (2001) Robust H ∞ control of distributed delay systems with application to combustion control. IEEE Trans Automat Control 46(12):1930–1935MathSciNetCrossRefMATH Xie L, Fridman E, Shaked U (2001) Robust H control of distributed delay systems with application to combustion control. IEEE Trans Automat Control 46(12):1930–1935MathSciNetCrossRefMATH
243.
252.
go back to reference Zheng F, Frank PM (2002) Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica 38:487–497CrossRefMATH Zheng F, Frank PM (2002) Robust control of uncertain distributed delay systems with application to the stabilization of combustion in rocket motor chambers. Automatica 38:487–497CrossRefMATH
Metadata
Title
Control Design for TDSs
Author
Emilia Fridman
Copyright Year
2014
DOI
https://doi.org/10.1007/978-3-319-09393-2_5