New approach to the design of robust tracking and model following controllers for uncertain delay systems

Abstract

For a class of uncertain time-delay systems, a new approach to the design of robust tracking and model following controllers is presented. In the case that the system uncertainties satisfy the generalised matching conditions, the resultant linear controller guarantees uniform ultimate boundedness of the tracking error, and furthermore the error bound can be made arbitrarily small. In the case of mismatched uncertainties, a sufficient condition is presented such that the controller ensures ultimate boundedness of the tracking error. The main feature of this approach is that much larger system uncertainties arising in the control matrix can be admitted. Two numerical examples are included to show the effectiveness of the approach

A Direct Approach to the Design of Robust Tracking Controllers for Uncertain Delay Systems

“…The tracking control is an important topic in control engineering practices [1][2][3][4][5][6][7]. Since time-delays are found to exist in many dynamical systems, for example, chemical processes and long transmission lines in pneumatic systems, and they frequently induce system instability, oscillations or degraded performances, the robust tracking control of uncertain time-delay systems has received considerable attention in recent years (see [4,6,7] and the references therein).…”

“…Since time-delays are found to exist in many dynamical systems, for example, chemical processes and long transmission lines in pneumatic systems, and they frequently induce system instability, oscillations or degraded performances, the robust tracking control of uncertain time-delay systems has received considerable attention in recent years (see [4,6,7] and the references therein). In [4], a linear robust tracking controller is presented for a class of uncertain time-delay systems.…”

“…In [4], a linear robust tracking controller is presented for a class of uncertain time-delay systems. By using a Riccati-type equation, the researchers develop an improved procedure for determining the controller such that larger uncertainties are accommodated in [6]. Very recently, using the common algebraic Riccati equation, Wu [5,7] has presented interesting results on the robust tracking and model following of uncertain dynamical systems with/without time delays.…”

“…It is noticed that the results of [4,6] are derived via the method of Lyapunov functionals instead of the Lyapunov functions or Razumikhin-type theorems which are custom-ary in the study of uncertain time-delay systems [8,9]. One may also note that the scheme of [4] is based on the solution of the Lyapunov equation while [6] employs a Riccatitype equation.…”

“…One may also note that the scheme of [4] is based on the solution of the Lyapunov equation while [6] employs a Riccatitype equation. However, both the Lyapunov equation and that Riccati-type equation request the nominal system matrix A to be asymptotically stable.…”