517.925; 517.93

control system, output feedback, robust stability, matrix uncertainty, ellipsoid.

New methods of robust stability analysis for equilibrium states and optimization of linear dynamic systems are developed. Sufficient stability conditions of the zero state are formulated for a linear control systems with uncertain coefficient matrices and measurable output feedback. In addition, a general quadratic Lyapunov function and ellipsoidal set of stabilizing matrices for the feedback amplification coefficients are given. Application of the results is reduced to solving the systems of linear matrix inequalities.

1. Polyak B. T., Shcherbakov P. S. Robastnaya ustoychivost’ i upravlenie. Moskva: Nauka, 2002. 303 p. [In Russian].
2. Zhou K., Doyle J. C., Glover K. Robust and optimal control, Englewood, Prentice Hall, 1996, 596 p.
3. Balandin D. V., Kogan M. M. Sintez zakonov upravleniya na osnove linejnyx matrichnyx neravenstv. Moskva: Fizmatlit, 2007. 280 p. [In Russian].
4. Kuncevich V. M. Upravlenie v usloviyax neopredelennosti: garantirovannye rezul'taty v zadachax upravleniya i identifikacii. Kiev: Nauk. Dumka, 2006, 264 p. [In Russian].
5. Mazko A. G. Robust stability and evaluation of the quality functional for nonlinear control systems. Automation and Remote Control. Vol. 76. No. 2. 2015. P. 251–263.
6. Aliluiko A. M., Ruska R. V. Robust stability of linear control system with matrix uncertainty. Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu. Vol. 82. No. 2. 2016, P. 128–136.
7. Polyak B. T., Shcherbakov P. S. Hard problems in linear control theory: Possible approaches to soltion, Automation and Remote Control. Vol. 66. No. 5. 2005. P. 681–718.
8. Aliev F.A., Larin V. B. Zadachi stabilizacii sistemy s obratnoj svyaz'yu po vyxodnoj peremennoj (obzor), Prikladnaya mexanika, Vol. 47. No. 3. 2011. P. 3–49. [In Russian].
9. Mazko A. G. Robastnaya ustojchivost' i stabilizaciya dinamicheskix sistem. Metody matrichnyx i konusnyx neravenstv. Kyiv: Instytut matematyky, 2016. 332 p. [In Russian].
10. Khlebnikov M. V., Shcherbakov P. S. Petersen’s lemma on matrix uncertainty and its generalizations, Automation and Remote Control. Vol. 69. No. 11. 2008. P. 1932–1945.
11. Petersen I. A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. Vol. 8. No. 4. 1987. P. 351–357.
12. Gantmaxer F. R. Teoriya matric. Мoskva: Nauka, 1988. 552 p. [In Russian].
13. Polyak B. T., Topunov M. V., Shherbakov P. S. Ideologiya invariantnyx e'llipsoidov v zadache o robastnom podavlenii ogranichennyx vneshnix vozmushhenij, Stoxasticheskaya optimizaciya v informatike. Vol. 3. 2007. P. 51–84.

1. Polyak B. T., Shcherbakov P. S. Robastnaya ustoychivost’ i upravlenie. Moskva: Nauka, 2002. 303 p. [In Russian].
2. Zhou K., Doyle J. C., Glover K. Robust and optimal control, Englewood, Prentice Hall, 1996, 596 p.
3. Balandin D. V., Kogan M. M. Sintez zakonov upravleniya na osnove linejnyx matrichnyx neravenstv. Moskva: Fizmatlit, 2007. 280 p. [In Russian].
4. Kuncevich V. M. Upravlenie v usloviyax neopredelennosti: garantirovannye rezul'taty v zadachax upravleniya i identifikacii. Kiev: Nauk. Dumka, 2006, 264 p. [In Russian].
5. Mazko A. G. Robust stability and evaluation of the quality functional for nonlinear control systems. Automation and Remote Control. Vol. 76. No. 2. 2015. P. 251–263.
6. Aliluiko A. M., Ruska R. V. Robust stability of linear control system with matrix uncertainty. Visnyk Ternopilskoho natsionalnoho tekhnichnoho universytetu. Vol. 82. No. 2. 2016, P. 128–136.
7. Polyak B. T., Shcherbakov P. S. Hard problems in linear control theory: Possible approaches to soltion, Automation and Remote Control. Vol. 66. No. 5. 2005. P. 681–718.
8. Aliev F.A., Larin V. B. Zadachi stabilizacii sistemy s obratnoj svyaz'yu po vyxodnoj peremennoj (obzor), Prikladnaya mexanika, Vol. 47. No. 3. 2011. P. 3–49. [In Russian].
9. Mazko A. G. Robastnaya ustojchivost' i stabilizaciya dinamicheskix sistem. Metody matrichnyx i konusnyx neravenstv. Kyiv: Instytut matematyky, 2016. 332 p. [In Russian].
10. Khlebnikov M. V., Shcherbakov P. S. Petersen’s lemma on matrix uncertainty and its generalizations, Automation and Remote Control. Vol. 69. No. 11. 2008. P. 1932–1945.
11. Petersen I. A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett. Vol. 8. No. 4. 1987. P. 351–357.
12. Gantmaxer F. R. Teoriya matric. Мoskva: Nauka, 1988. 552 p. [In Russian].
13. Polyak B. T., Topunov M. V., Shherbakov P. S. Ideologiya invariantnyx e'llipsoidov v zadache o robastnom podavlenii ogranichennyx vneshnix vozmushhenij, Stoxasticheskaya optimizaciya v informatike. Vol. 3. 2007. P. 51–84.