Output regulation for non‐square linear multi‐rate systems

We address the problem of regulating a subset of outputs of a linear time-invariant plant with multi-rate measurements so as to achieve asymptotic tracking of an exogenous signal generated by the free motion of a linear time-invariant system, denoted by exosystem. A solution to this problem is required to yield closedloop stability and should be such that output regulation is achieved even in the presence of small plant uncertainties and exogenous disturbances also generated by the exosystem. Contrarily to previous works, we propose a solution to the general case where the plant may have more measured outputs than inputs. We show that this solution allows us to solve simultaneous stabilization and output regulation problems that are not possible to solve through the previous works. Besides incorporating an internal model of the exosystem, the key feature of our proposed controller is that it includes a system that blocks signals generated by the exosystem arriving to the controller from the non-regulated outputs. Copyright c © 2011 John Wiley & Sons, Ltd.

[1]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[2]  R. Scattolini,et al.  LQG optimal control of multirate sampled-data systems , 1992 .

[3]  G. Basile,et al.  Controlled and conditioned invariants in linear system theory , 1992 .

[4]  Patrizio Colaneri,et al.  Invariant representations of discrete-time periodic systems , 2000, Autom..

[5]  P. Colaneri.  Output stabilization via pole placement of discrete-time linear periodic systems , 1991 .

[6]  Patrizio Colaneri,et al.  Stabilization of multirate sampled-data linear systems , 1990, Autom..

[7]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[8]  Christopher I. Byrnes,et al.  Output regulation for nonlinear systems: an overview , 2000 .

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

[10]  W. Wonham,et al.  Regulation and Internal Stabilization in Linear Multivariable Systems , 1974 .

[11]  Riccardo Scattolini,et al.  Stabilization, Regulation, and Optimization of Multirate Sampled-Data Systems , 1995 .

[12]  Rita Cunha,et al.  On the design of multi‐rate tracking controllers: Application to rotorcraft guidance and control , 2010 .

[13]  D. Lawrence,et al.  Output regulation for linear systems with sampled measurements , 2001, Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148).

[14]  J. Doyle,et al.  Robust and optimal control , 1995, Proceedings of 35th IEEE Conference on Decision and Control.

[15]  Rita Cunha,et al.  Linear Parameter Varying Control for Sampled-data Multi-rate Systems , 2008 .

[16]  Riccardo Scattolini,et al.  On the output control of multirate systems subject to arbitrary exogenous signals , 1993, IEEE Trans. Autom. Control..

[17]  E. Davison.  The output control of linear time-invariant multivariable systems with unmeasurable arbitrary disturbances , 1972 .

[18]  Sauro Longhi,et al.  Structural properties of multirate sampled-data systems , 1994, IEEE Trans. Autom. Control..

[19]  Paolo Bolzern,et al.  Stabilizability and detectability of linear periodic systems , 1985 .