H_∞ Model Reduction for Positive Fractional Order Systems

Abstract

This paper focuses on the H• model reduction problem of positive fractional order systems. For a stable positive fractional order system, we aim to construct a positive reduced-order fractional system such that the associated error system is stable with a prescribed H• performance. Then, based on the bounded real lemma for fractional order systems, a sufficient condition is given to characterize the model reduction problem with a prescribed H•-norm error bound in terms of a linear matrix inequality (LMI). Furthermore, by introducing a new flexible real matrix variable, the desired reduced-order system matrices are decoupled with the complex matrix variable and further parameterized by the new matrix variable. A corresponding iterative LMI algorithm is also proposed. Finally, several illustrative examples are given to show the effectiveness of the proposed algorithms.

Dominant pole and eigenstructure assignment for positive systems with state feedback

“…One can see that the positivity of a system not only imposes restrictions, but also leads to unique features which can be utilised when investigating the system. This also applies to positive systems other than LTI positive systems, for example, see Liu and Lam (2013) and Zhu, Meng, and Zhang (2013) for positive systems with delays, and Kaczorek (2013) and Shen and Lam (2014a) for fractional order positive systems.…”

Finite-frequency model order reduction of discrete-time linear time-delayed systems

“…Step 2 Solve the following LMI-based optimization problem min γ subject to (11), (24) Step 3 If the optimization problem in Step 2 is feasible, then the reduced-order model (A r , A dr , B r , C r , C dr , D r ) can be obtained by (12).…”

“…By adopting the LMI-based techniques, the approximation performance in various senses (such as H ∞ , H 2 ) can be converted into a solvable convex optimization problem. This makes the LMI optimization method prevail for model reduction problems with respect to linear systems with/without additional complex dynamical phenomena [11][12][13][14][15][16].…”

Pressure Pump Power Control in the Primary Circuit of the Heat Exchange System

“…In its turn the volume of the incoming coolant depends on the position of the controlled stem valve h, which is set by the drive. To use traditional PID controls it is enough to organize two circuits [2] the first one sets the valve position, the second one, including PID, calculates the specified position of the rod on the mismatch between the target Tset and the measured temperature Tpd2 values.…”