=. Modeltitle, Problem1

, SiconosVector init_state_r (new SiconosVector

, SP:: SiconosVector control (new SiconosVector, issue.1

. Ls_a?>setvalue,

, 25 SP::SimpleMatrix Int_B

. Int_d?>setvalue,

, 41 dataPlot (0,1) = xinit_r

, 42 dataPlot (0,2) = xinit

, FirstOrderLinearDS LSCircuitRLCD(new FirstOrderLinearTIDS( init_state_r

, 52 SP:: FirstOrderLinearTIR LTIRCircuitRLCD(new FirstOrderLinearTIR

?. Ltircircuitrlcd and . >setdptr,

?. Ltircircuitrlcd and . >seteptr,

, 55 SP::NonSmoothLaw NSLaw(new ComplementarityConditionNSL

, 56 SP:: Interaction InterCircuitRLCD(new Interaction

, NonSmoothDynamicalSystem CircuitRLCD

, // dataPlot ( j +1, 0) = CircuitRLCD?>t0

. //-circuitrlcd?>settitle,

?. Circuitrlcd and . >insertdynamicalsystem, LSCircuitRLCD

?. Circuitrlcd and . >link,

?. Intercircuitrlcd and . >computeoutput,

?. Intercircuitrlcd and . >computeinput,

/. , CircuitRLCD?>display(

/. , EulerMoreauOSI(theta), issue.1

/. , ) Time discretisation ?? 71 SP:: TimeDiscretisation TiDiscRLCD(new TimeDiscretisation(t0, h_step

. //-???,

, Simulation setup with, SP::TimeStepping StratCircuitRLCD(new TimeStepping(CircuitRLCD, p.76

, 77 double h = StratCircuitRLCD?>timeStep(

. //-boost,

, // t . restart (

, StratCircuitRLCD?>computeOneStep(

, )<<endl

, ?theta) * ( * init_state_r ) (0) )+( * control_r

, +1, 1) = ( * LSCircuitRLCD?>x(

, Compute state x 87 88 SP::FirstOrderLinearDS LSCircuitRLCD1(new FirstOrderLinearTIDS(init_state, vol.1

, 89 SP:: FirstOrderLinearTIR LTIRCircuitRLCD1(new FirstOrderLinearTIR(Int_C1, Int_B

?. Ltircircuitrlcd1 and . &gt;setdptr,

?. Ltircircuitrlcd1 and . &gt;seteptr,

, ComplementarityConditionNSL, issue.1

, 93 SP:: Interaction InterCircuitRLCD1(new Interaction (NSLaw1, LTIRCircuitRLCD1

, NonSmoothDynamicalSystem CircuitRLCD1

. //-circuitrlcd?&gt;settitle,

?. Circuitrlcd1 and . &gt;insertdynamicalsystem,

?. Circuitrlcd1 and . &gt;link,

/. , ) OneStepIntegrators ?? 105 SP::EulerMoreauOSI OSI_RLCD1

/. , ) Time discretisation ?? 108 SP:: TimeDiscretisation TiDiscRLCD1(new TimeDiscretisation(t0, h_step

. //-???,

, Simulation setup with

, 116 boost :: timer t1

, StratCircuitRLCD1?>computeOneStep(

!. //solve and . Ls_a?&gt;setvalue,

. Ls_a?&gt;setvalue,

. Ls_a?&gt;setvalue, , p.1

. Ls_a?&gt;setvalue,

, 34 SP::SimpleMatrix Int_B(new SimpleMatrix

. Int_b?&gt;setvalue,

, 39 SP::SimpleMatrix Int_C(new SimpleMatrix

. Int_c?&gt;setvalue,

, 44 SP::SimpleMatrix Int_D(new SimpleMatrix

, 45 SP::SimpleMatrix LS_A1(new SimpleMatrix

, SimpleMatrix dataPlot

, 56 dataPlot (0,1) = xinit_r

, 57 dataPlot (0,2) = xinit_r1

, 58 dataPlot (0,3) = xinit

, 59 dataPlot (0,4) = xinit1

T. ,

, control_r ?>setValue(1, theta * sin (T)+(1?theta) * sin

, // First round 70 SP::FirstOrderLinearDS LSCircuitRLCD(new FirstOrderLinearTIDS( init_state_r

, 71 SP:: FirstOrderLinearTIR LTIRCircuitRLCD(new FirstOrderLinearTIR

?. Ltircircuitrlcd and . &gt;setdptr,

/. &gt;seteptr,

, 74 SP::NonSmoothLaw NSLaw(new ComplementarityConditionNSL

, 75 SP:: Interaction InterCircuitRLCD(new Interaction

, NonSmoothDynamicalSystem CircuitRLCD

, // dataPlot ( j +1, 0) = CircuitRLCD?>t0

. //-circuitrlcd?&gt;settitle,

?. Circuitrlcd and . &gt;insertdynamicalsystem, LSCircuitRLCD

?. Circuitrlcd and . &gt;link,

?. Intercircuitrlcd and . &gt;computeoutput,

?. Intercircuitrlcd and . &gt;computeinput,

/. , CircuitRLCD?>display(

/. , ) OneStepIntegrators ?? 86 SP::EulerMoreauOSI OSI_RLCD

/. , ) Time discretisation ?? 89 SP:: TimeDiscretisation TiDiscRLCD(new TimeDiscretisation(t0, h_step

. //-???,

, Simulation setup with, SP::TimeStepping StratCircuitRLCD(new TimeStepping(CircuitRLCD, p.94

, 95 double h = StratCircuitRLCD?>timeStep(

, 96 boost :: timer t

, t . restart (

, StratCircuitRLCD?>computeOneStep(

, )<<endl

, 100 ( * control ) (0) = 0

, ) = ?theta * (k1 * ( * LSCircuitRLCD?>x())(0)+k2 * ( * LSCircuitRLCD?>x(

, ?theta) * (k1 * ( * init_state_r ) (0)+k2 * ( * init_state_r ) (1) )+( * control_r

, 104 init_state_r ?>setValue, issue.1

, 106 dataPlot ( j +1, 1) = ( * LSCircuitRLCD?>x())(0)

, 107 dataPlot ( j +1, 2) = ( * LSCircuitRLCD?>x())(1)

, // Second round 109 SP::FirstOrderLinearDS LSCircuitRLCD1(new FirstOrderLinearTIDS

, 110 SP:: FirstOrderLinearTIR LTIRCircuitRLCD1(new FirstOrderLinearTIR

?. Ltircircuitrlcd1 and . &gt;setdptr,

/. &gt;seteptr,

, 113 SP::NonSmoothLaw NSLaw1(new ComplementarityConditionNSL

, 114 SP:: Interaction InterCircuitRLCD1(new Interaction (NSLaw1, LTIRCircuitRLCD1

, NonSmoothDynamicalSystem CircuitRLCD1

. //-circuitrlcd?&gt;settitle,

?. Circuitrlcd1 and . &gt;insertdynamicalsystem,

?. Circuitrlcd1 and . &gt;link,

/. , EulerMoreauOSI(theta), issue.1

/. , ) Time discretisation ?? 127 SP:: TimeDiscretisation TiDiscRLCD1(new TimeDiscretisation(t0, h_step

. //-???,

, Simulation setup with

V. Acary and B. Brogliato, Numerical Methods for Nonsmooth Dynamical Systems: Applications in Mechanics and Electronics, vol.35, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00423530

S. Adly, A Variational Approach to Nonsmooth Dynamics: Applications in Unilateral Mechanics and Electronics, 2017.

B. Brogliato and D. Goeleven, Well-posedness, stability and invariance results for a class of multivalued Lur'e dynamical systems, Nonlinear Analysis, Theory, Methods, and Applications, vol.74, pp.195-212, 2011.
URL : https://hal.archives-ouvertes.fr/inria-00442081

B. Brogliato, R. Lozano, B. Maschke, and O. Egeland, Dissipative Systems Analysis and Control, Theory and Applications, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00821748

B. Brogliato and L. Thibault, Existence and uniqueness of solutions for nonautonomous complementarity dynamical systems, Journal of Convex Analysis, vol.17, issue.3-4, pp.961-990, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00756226

M. K. Camlibel, W. P. Heemels, and J. M. Schumacher, On linear passive complementarity systems, European Journal of Control, vol.8, issue.3, pp.220-237, 2002.

P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox For Use with MATLAB

D. Goeleven, D. Montreanu, and V. V. Montreanu, On the stability of stationary solutions of first order evolution variational inequalities, Advances in Nonlinear Variational inequalities, vol.6, pp.1-30, 2013.

W. P. Heemels and B. Brogliato, The complementarity class of hybrid dynamical systems, European Journal of Control, vol.9, issue.2-3, pp.322-360, 2003.

K. G. Murty, Linear Complementarity, Linear and Nonlinear Programming, 1988.