Synthesis of Sector-Bounded Control : General Approach of $H{\infty}$ Control and Positive Real Control

$H{\infty}$제어와 양실 제어의 일반형태인 구간영역제어기의 설계

  • 심덕선 (중앙대학교 전자전기공학부)
  • Published : 1999.01.01

Abstract

We consider the problem of synthesizing an internally stabilizing linear time-invariant controller for a linear tune-Invariant plant such that a given closed loop transfer function is strictly sector bounded. We show that the standard $H{\infty}$ control problem and the $\tau$ -positive real control problem are special cases of sector bounded control problem. Necessary and sufficient conditions for the existence of a controller are obtained. The state-space representation for strictly proper controllers are given in terms of solutions to ARIs or AREs.

Keywords

References

  1. International Journal of Control v.45 no.3 Synthesis of positive real multivariable feedback systems M.G.Sofonove;E.A.Jonckheere
  2. Proc. 35th IEEE Conference on Decision and Control Synthesis of r-positive real feedback systems N.Sakamoto;M.Sugiura;M.Hayashi;M.Suzuki
  3. Proc. 33rd IEEE Conference on Decision and Control Some properties and stability results for sector-bounded LTI systems Gupta;S.M.Joshi
  4. IEEE Trans. Automatic Control v.11 no.2;3 On the input-output stability of time-varying nonlinear feedback systems G.Zames
  5. Network Analysis and Synthesis: A Modern Systems Theory Approach B.D.O.Anderson;S.Vongpanitlerd
  6. Systems & Control Letters v.17 no.3 Robust Stabilization with Positive real uncertainty: Beyond the small gain theorem W.W.Haddad;D.S.Bernstein
  7. IEEE Trans. Automatic Control v.39 Solution to the positive real control problem for linear time-invariant systems W.Sun;P.P.Pramod;D.Shim
  8. Systems & Control Letters v.11 An algebraic Riccati equation approach to H∞ optimization K.Zhou;P.P.Khargonekar
  9. Systems & Control Letters v.9 Matrix Riccati inequality: existence of solutions L.E.Faibusovich
  10. Linear Algebra and its Applications v.99 Existence and comparison theorems for algebraic Riccati equations for continuous and discrete-time systems A.C.M.Ran;R.Vreugdenhil
  11. IEEE Trans. Automatic Control v.34 no.8 State-space solutions to standard H₂and H∞ control problems J.C.Doyle;K.Glover;P.P.Khargonekar;B.francis
  12. Proc. American Control Conference State space characterization and robust stabilization of dissipative LTI systems S.Gupta;S.M.Joshi
  13. Journal of the Franklin Institute v.309 no.5 Dissipative dynamic systems: basic input-output and state proe-prties D.J.Hill;P.J.Moylan
  14. Archive for rational Mechanics and Analysis v.45 no.5 Dissipative dynamic systems, part I: general theory J.C.Willems
  15. Archive for rational Mechanics and Analysis v.45 no.5 Dissipative dynamic systems, part Ⅱ: linear systems with quadratic supply rates J.C.Willems