Robust control of linear time-invariant plants using periodic compensation

This paper considers the use and design of linear periodic time-varying controllers for the feedback control of linear time-invariant discrete-time plants. We will show that for a large class of robustness problems, periodic compensators are superior to time-invariant ones. We will give explicit design techniques which can be easily implemented. In the context of periodic controllers, we also consider the strong and simultaneous stabilization problems. Finally, we show that for the problem of weighted sensitivity minimization for linear time-invariant plants, time-varying controllers offer no advantage over the time-invariant ones.

[1]  F. J. Mullin,et al.  The analysis of sampled-data control systems with a periodically time-varying sampling rate , 1959, IRE Transactions on Automatic Control.

[2]  W. Rudin.  Real and complex analysis , 1968 .

[3]  Jon H. Davis.  Stability Conditions Derived from Spectral Theory: Discrete Systems with Periodic Feedback , 1972 .

[4]  D. Youla,et al.  Single-loop feedback-stabilization of linear multivariable dynamical plants , 1974, Autom..

[5]  C. Desoer,et al.  The feedback interconnection of lumped linear time-invariant systems☆ , 1975 .

[6]  C. Sidney Burrus,et al.  A unified analysis of multirate and periodically time-varying digital filters , 1975 .

[7]  B. O. Anderson,et al.  Time-varying feedback laws for decentralized control , 1980, 1980 19th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[8]  A. Tannenbaum.  Feedback stabilization of linear dynamical plants with uncertainty in the gain factor , 1980 .

[9]  George Zames,et al.  A new approach to classical frequency methods: Feedback and minimax sensitivity , 1981, 1981 20th IEEE Conference on Decision and Control including the Symposium on Adaptive Processes.

[10]  G. Stein,et al.  Multivariable feedback design: Concepts for a classical/modern synthesis , 1981 .

[11]  M. Athans,et al.  Robustness results in linear-quadratic Gaussian based multivariable control designs , 1981 .

[12]  G. Zames.  Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses , 1981 .

[13]  Shih-Ho Wang,et al.  Stabilization of decentralized control systems via time-varying controllers , 1982 .

[14]  M. Vidyasagar,et al.  Algebraic design techniques for reliable stabilization , 1982 .

[15]  J. Murray,et al.  Fractional representation, algebraic geometry, and the simultaneous stabilization problem , 1982 .

[16]  G. Zames,et al.  Feedback, minimax sensitivity, and optimal robustness , 1983 .

[17]  H. Kimura.  Robust stabilizability for a class of transfer functions , 1983, The 22nd IEEE Conference on Decision and Control.

[18]  J. Doyle.  Synthesis of robust controllers and filters , 1983, The 22nd IEEE Conference on Decision and Control.

[19]  Bor-Chin Chang,et al.  Optimal disturbance reduction in linear multivariable systems , 1983 .

[20]  Christopher I. Byrnes,et al.  Simultaneous stabilization and simultaneous pole-placement by nonswitching dynamic compensation , 1983 .

[21]  G. Zames,et al.  H ∞ -optimal feedback controllers for linear multivariable systems , 1984 .

[22]  Bruce A. Francis,et al.  Uniformly optimal control of linear time-varying systems , 1984 .

[23]  Bruce A. Francis,et al.  Uniformly optimal control of linear feedback systems , 1985, Autom..

[24]  P. Khargonekar,et al.  Non-Euclidian metrics and the robust stabilization of systems with parameter uncertainty , 1985 .