Robust state-derivative feedback LMI-based designs for multivariable linear systems

In some practical problems, for instance in the control systems for the suppression of vibration in mechanical systems, the state-derivative signals are easier to obtain than the state signals. New necessary and sufficient linear matrix inequalities (LMI) conditions for the design of state-derivative feedback for multi-input (MI) linear systems are proposed. For multi-input/multi-output (MIMO) linear time-invariant or time-varying plants, with or without uncertainties in their parameters, the proposed methods can include in the LMI-based control designs the specifications of the decay rate, bounds on the output peak, and bounds on the state-derivative feedback matrix K. These design procedures allow new specifications and also, they consider a broader class of plants than the related results available in the literature. The LMIs, when feasible, can be efficiently solved using convex programming techniques. Practical applications illustrate the efficiency of the proposed methods.

[1]  M. Teixeira,et al.  Design of SPR Systems with Dynamic Compensators and Output Variable Structure Control , 2006, International Workshop on Variable Structure Systems, 2006. VSS'06..

[2]  E. Fridman,et al.  H∞-control of linear state-delay descriptor systems: an LMI approach , 2002 .

[3]  E. Assuncao,et al.  A global optimization approach for the H/sub 2/-norm model reduction problem , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[4]  C. Q. Andrea,et al.  H/sub 2/ and H/sub /spl infin// -optimal control for the tracking problem with zero variation , 2007 .

[5]  Michel Verhaegen,et al.  Robust output-feedback controller design via local BMI optimization , 2004, Autom..

[6]  Eduard Reithmeier,et al.  Robust vibration control of dynamical systems based on the derivative of the state , 2003 .

[7]  Reinaldo M. Palhares,et al.  Discussion on: "H Output Feedback Control Design for Uncertain Fuzzy Systems with Multiple Time Scales: An LMI Approach" , 2005, Eur. J. Control.

[8]  T.G. Habetler,et al.  High-performance induction motor speed control using exact feedback linearization with state and state derivative feedback , 2003, IEEE Transactions on Power Electronics.

[9]  Haiying Jing.  Eigenstructure assignment by proportional-derivative state feedback in singular systems , 1994 .

[10]  R. Takahashi,et al.  Improved optimisation approach to the robust H2/H∞ control problem for linear systems , 2005 .

[11]  Yi-Qing Ni,et al.  State‐Derivative Feedback Control of Cable Vibration Using Semiactive Magnetorheological Dampers , 2005 .

[12]  T.G. Habetler,et al.  High-performance induction motor speed control using exact feedback linearization with state and state derivative feedback , 2003, IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC '03..

[13]  Laurent El Ghaoui,et al.  Advances in linear matrix inequality methods in control: advances in design and control , 1999 .

[14]  Reinaldo M. Palhares,et al.  Discussion on: “H∞ Output Feedback Control Design for Uncertain Fuzzy Systems with Multiple Time Scales: An LMI Approach” , 2005 .

[15]  Marcelo C. M. Teixeira,et al.  On relaxed LMI-based designs for fuzzy regulators and fuzzy observers , 2001, 2001 European Control Conference (ECC).

[16]  Gregory N. Washington,et al.  Acceleration Feedback-Based Active and Passive Vibration Control of Landing Gear Components , 2002 .

[17]  M. Valasek,et al.  Pole-placement for SISO linear systems by state-derivative feedback , 2004 .

[18]  Michael Valásek,et al.  Direct algorithm for pole placement by state-derivative feedback for multi-inputlinear systems - nonsingular case , 2005, Kybernetika.

[19]  Yurii Nesterov,et al.  Interior-point polynomial algorithms in convex programming , 1994, Siam studies in applied mathematics.

[20]  Gregory N. Washington,et al.  Acceleration-based vibration control of distributed parameter systems using the reciprocal state-space framework , 2002 .

[21]  Pedro Luis Dias Peres,et al.  Global optimization for the -norm model reduction problem , 2007, Int. J. Syst. Sci..

[22]  Guang-Ren Duan,et al.  REGULARIZABILITY OF LINEAR DESCRIPTOR SYSTEMS VIA OUTPUT PLUS PARTIAL STATE DERIVATIVE FEEDBACK , 2008 .

[23]  R. M. PALHARES,et al.  Robust H ∞ Fuzzy Filtering for a Class of State-Delayed Nonlinear Systems in an LMI Setting , 2002 .

[24]  George W. Irwin,et al.  Robust stabilization of descriptor linear systems via proportional-plus-derivative state feedback , 1999, Proceedings of the 1999 American Control Conference (Cat. No. 99CH36251).