This page provides the MatLab codes (.m files) of  LMI conditions published in recent papers of my authoring (or co-authoring). The routines run under the MatLab environment and require YALMIP as the LMI parser and SeDuMi as the LMI solver. If you use the programs in your research, paper or thesis, please acknowledge this page.



Important: This page has not been updated since long time. The reason is that any parameter-dependent LMI with parameters lying in the unit simplex or in a hyperrectangle can be systematically treated in a high level programming language, implemented in the Matlab (or Octave) toolbox Robust LMI Parser - ROLMIP. Please, visit the ROLMIP website for more information. See also the paper.


(OP05)- R. C. L. F. Oliveira and P. L. D. Peres. Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions. Linear Algebra and Its Applications, 405:209-228, August 2005.

Theorem 3 (Hurwitz)	estab_OP05_LAA_T3_yal.m
Theorem 4 (Schur)	estab_OP05_LAA_T4_yal.m
Theorem 5  (Hurwitz)	estab_OP05_LAA_T5_c_yal.m
Theorem 5 (Schur)	estab_OP05_LAA_T5_d_yal.m

                                                   * The database of stable polytopes used in the exhaustive simulations is also available under request.


(OP06)- R. C. L. F. Oliveira and P. L. D. Peres. LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions. Systems & Control Letters, 55:52-61, January 2006.

Theorem 1	estab_OP06_SCL_T1_yal.m
Theorem 2	estab_OP06_SCL_T2_yal.m
Theorem 3	estab_OP06_SCL_T3_yal.m
Theorem 4	estab_OP06_SCL_T4_yal.m
Data Example 1	ex_estab_c_OP06a_ex1
Data Example 2	ex_estab_c_OP06a_ex2
Data Example 3	ex_estab_c_OP06a_ex3
Data Example 4	ex_estab_d_OP06a_ex4
Data Example 5	ex_estab_d_OP06a_ex5

                                                   * The database of stable polytopes used in section 4.1 is also available under request.

(OP07)- R. C. L. F. Oliveira and P. L. D. Peres. Parameter-dependent LMIs in robust analysis: characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations. IEEE Transactions on Automatic Control, 52(7):1334-1340, July 2007.

Theorem 2	estab_OP07_IEEETAC_T2_yal.m
Theorem 3	estab_OP07_IEEETAC_T3_yal.m
Theorem 4 (Hurwitz)	estab_OP07_IEEETAC_T4_c_yal.m
Theorem 4 (Schur)	estab_OP07_IEEETAC_T4_d_yal
Data Example 1	ex_estab_d_OP07_ex1.m
Data Example 2	ex_estab_c_OP07_ex2.m

(MOPB07)- V. F. Montagner, R. C. L. F. Oliveira, P. L. D. Peres and P.-A. Bliman. Linear matrix inequality characterisation for  H-infinity and H-2 guaranteed cost gain-scheduling quadratic stabilisation of linear time-varying polytopic systems. IET Control Theory & Applications, 1(6):1726-1735, November 2007.                                          

Theorem 2 (stabilization)	synth_stab_MOPB07_IET_T2_yal.m
Theorem 3 (H-infinity)	synth_hinf_MOPB07_IET_T3_yal
Theorem 4 (H-2 primal)	synth_h2_P_MOPB07_IET_T4_yal
Theorem 3 (H-2 dual)	synth_h2_D_MOPB07_IET_T4_yal
Example 2	run_MOPB07_example_2.m, data_MOPB07_example_2.mat
Example 3	run_MOPB07_example_3.m,  data_AC5_COMPleib.mat

(OP08a)- R. C. L. F. Oliveira and  P. L. D. Peres. Robust stability analysis and control design for time-varying discrete-time polytopic systems with bounded parameter variation.  In Proceedings of the 2008 American Control Conference, pages 3094-3099, Seattle, WA, USA, June 2008.         

Theorem 2 (robust  stability)	stab_OP08a_ACC_T2_yal.m
Theorem 3 (robust synthesis)	synth_rob_OP08a_ACC_T3_yal.m
Theorem 4 (Gain-scheduling synthesis:	synth_GS_OP08a_ACC_T4_yal.m

(BMOPB08)- R. A. Borges, V. F. Montagner, R. C. L. F. Oliveira, P. L. D. Peres and P.-A. Bliman. Parameter-dependent H-2 and H-infinity filter design for linear systems with arbitrarily time-varying parameters in polytopic domains. Signal Processing, 88(7):1801-1816, July 2008.                                            

Theorem 2 (H-infinity)	hinf_BMOPB08_SIGPRO_T1_yal
Theorem 3 (H-2 primal)	h2_BMOPB08_SIGPRO_T2p_yal
Theorem 3 (H-2 dual)	h2_BMOPB08_SIGPRO_T2d_yal
Example 1	data_example1_BMOPB07.mat
Example 2	data_example2_BMOPB07.mat
Example 3	data_example3_BMOPB07.mat

(OP08b)- R. C. L. F. Oliveira and P. L. D. Peres. A convex optimization procedure to compute H-2 and H-infinity norms for uncertain linear systems in polytopic domains . Optimal Control Applications and Methods, 29(4):295-312, July/August 2008.

Theorem 1	hinf_OP08b_OCAM_T1_yal.m
Theorem 2	hinf_OP08b_OCAM_T2_yal.m
Theorem 3 (cont.)	hinf_OP08b_OCAM_T3_c_yal.m
Theorem 3 (disc.)	hinf_OP08b_OCAM_T3_d_yal.m
Theorem 4	h2_OP08b_OCAM_T4_yal.m
Theorem 5	h2_OP08b_OCAM_T5_yal.m
Theorem 6 (cont.)	h2_OP08b_OCAM_T6_c_yal.m
Theorem 6 (disc.)	h2_OP08b_OCAM_T6_d_yal.m

(OdOP08)- R. C. L. F. Oliveira, M. C. de Oliveira and P. L. D. Peres. Convergent LMI relaxations for robust analysis of uncertain linear systems using lifted polynomial parameter-dependent Lyapunov functions. Systems & Control Letters, 57:680-689, August 2008.

Theorem 3 (robust analysis)	stab_OdOP08_SCL_T8_yal
Theorem 4 (H-2 analysis)	h2_OdOP08_SCL_T11_yal
Theorem 4* (H-2 analysis, Pk constant)	h2_OdOP08_SCL_T11_star_yal
Example 2	data_ex2_OdOP08_SCL.mat

                                                   * The database of stable polytopes used in Example 1 is also available under request.


(OBP08)- R. C. L. F. Oliveira, P.-A. Bliman and  P. L. D. Peres. Robust LMIs with parameters in multi-simplex: Existence of solutions and applications. Proceedings of the 47th IEEE Conference on Decision and Control, pages 2226-2231, Cancun, Mexico, December 2008.

Theorem 2 (time-invariant case)	stab_OBP08_CDC_T2_yal.m
Theorem 3 (time-varying case)	stab_OBP08_CDC_T3_yal.m
Auxiliary and useful routines:	affine2MS_LTI.m    affine2MS_LTV.m    create_MSpolynomial.m    multiply_MSpoly.m

(OVdVP09)- R. C. L. F. Oliveira, A. N. Vargas, J. B. R. do Val and P. L. D. Peres. Robust stability, H-2 analysis and stabilisation of discrete-time Markov jump linear systems with uncertain probability matrix. International Journal of Control, 82(3):470-481, March 2009. 

Theorem 2 (analysis)	h2_MJLS_OVdVP09_IJC_T2_yal.m
Theorem 3 (analysis)	h2_MJLS_OVdVP09_IJC_T3_yal.m
Theorem 4 (synthesis mod. dep.)	synth_h2_MJLS_OVdVP09_IJC_T4_yal.m
Corollary 3 (synthesis mod. indep)	synth_h2_MJLS_OVdVP09_IJC_C3_yal
Data Example 1	data_ex1_OVdVP09.mat
Data Example 2	data_ex2_OVdVP09.mat
Data Example 3	data_ex3_OVdVP09.mat

(MOPB09)- V. F. Montagner, R. C. L. F. Oliveira, P. L. D. Peres and P.-A. Bliman. Stability analysis and gain-scheduled state feedback
control for systems with bounded parameter variations. International Journal of Control, 82(6):1045-1059, June 2009.

Theorem 1	stab_MOPB09_IJC_T1_c_yal.m
Theorem 2	stab_MOPB09_IJC_T2_c_yal.m
Corollary 3	stab_MOPB09_IJC_C3_c_yal.m
Corollary 4	stab_MOPB09_IJC_C4_c_yal.m
Corollary 5	stab_MOPB09_IJC_C5_c_yal.m
Theorem 3 (design)	synth_MOPB09_IJC_T3_c_yal.m
Example 4	run_MOPB09_ex4.m

(MOP09a)- V. F. Montagner, R. C. L. F. Oliveira and P. L. D. Peres. Convergent LMI relaxations for quadratic stabilizability and H-infinity control of Takagi-Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 2007,17(4):863-873, August 2009. 

Theorem 2 (stabilization)	ssf_stabTS_MOP09_T2_yal.m
Theorem 3 (H-infinity control)	ssf_hinfTS_MOP09_T3_yal.m
Example 1	system_example_1.m
Example 2	data_example_2

(OBP09)- R. C. L. F. Oliveira, P.-A. Bliman and  P. L. D. Peres. Selective gain-scheduling for continuous-time linear systems with parameters in multi-simplex. Proceedings of the European Control Conference 2009, pages 213-218, Budapest, Hungary, August 2009.

Theorem 1 (stabilization)	stabMS_OBP09_ECC_T1_yal.m
Theorem 2 (H-2 control)	h2MS_OBP09_ECC_T1_yal.m
Theorem 3 (H-infinity control)	hinfMS_OBP09_ECC_T1_yal.m
Auxiliary and useful routines:	affine2MS_LTI.m    affine2MS_LTV.m    create_MSpolynomial.m    multiply_MSpoly.m

(OdOP09)- R. C. L. F. Oliveira, M. C. de Oliveira and  P. L. D. Peres. A special time-varying Lyapunov function for robust stability analysis of LPV systems with bounded parameter variation. IET Control Theory & Applications, 3(10):1448-1461, October 2009.

Theorem 2  (structure C1)	stabLPV_OdOP_IETCTA_C1_yal.m
Theorem 2  (structure C2)	stabLPV_OdOP_IETCTA_C2_yal.m
Theorem 2 (structure C3)	stabLPV_OdOP_IETCTA_C3_yal.m
Theorem 2 (structure C1_bar)	stabLPV_OdOP_IETCTA_C1b_yal.m
Theorem 2 (structure C3_bar)	stabLPV_OdOP_IETCTA_C3b_yal.m
Example 3	run_example_OdOP_IETCTA_ex3.m

(OP09)- R. C. L. F. Oliveira and  P. L. D. Peres. Time-varying discrete-time linear systems with bounded rates of variation: Stability analysis and control design.   Automatica, 45(11):2620-2626, November 2009.

Theorem 2 (stability - HPPD)	stab_OP10_AUT_T2_yal.m
Theorem 3 (stability - path-dep.)	stab_OP10_AUT_T3_yal.m
Theorem 4 (design rob. - HPPD)	design_OP10_AUT_T4_yal.m
Theorem 4m (design rob. - path-dep.)	design_OP10_AUT_T4m_yal.m
Theorem 5 (design GS - HPPD)	design_OP10_AUT_T5_yal.m
Theorem 5m (design GS - path-dep.)	design_OP10_AUT_T5m_yal.m
Auxiliarly routines (mandatory for the above routines)	alpha2gamma_HPPD.m alpha2gamma_path.m

(TOP11b)- T. S. Tognetti, R. C. L. F. Oliveira and  P. L. D. Peres. Selective H-2 and H-infinity stabilization of Takagi-Sugeno fuzzy systems.   IEEE Transactions on Fuzzy Systems, 19(5):890-900, October 2011.

Theorem 2	synth_tfs_TOP11b_T2_yal.m
Example 2	Example 2.m