New robust LMI synthesis conditions for mixed  gain‐scheduled reduced‐order DOF control of discrete‐time LPV systems

Abstract

Summary This paper investigates the problems of stabilization and mixed H2false/H∞ reduced‐order dynamic output‐feedback control of discrete‐time linear systems. The synthesis conditions are formulated in terms of parameterdependent linear matrix inequalities (LMIs) combined with scalar parameters, dealing with state‐space models where the matrices depend polynomially on time‐varying parameters and are affected by norm‐bounded uncertainties. The motivation to handle these models comes from the context of networked control systems, particularly when a continuous‐time plant is controlled by a digitally implemented controller. The main technical contribution is a distinct LMI‐based condition for the dynamic output‐feedback problem, allowing an arbitrary structure (polynomial of arbitrary degree) for the measured output matrix. Additionally, an innovative heuristic is proposed to reduce the conservativeness of the stabilization problem. Numerical examples are provided to illustrate the potentialities of the approach to cope with several classes of discrete‐time linear systems (time‐invariant and time‐varying) and the efficiency of the proposed design conditions when compared with other methods available in the literature.

Linear matrix inequality‐based solution for memory static output‐feedback control of discrete‐time linear systems affected by time‐varying parameters

“…For this purpose, stabilization tests were performed using a database of time‐invariant polytopic systems composed by open loop unstable systems, proposed by Morais et al, 43 which are guaranteed to be stabilized by some robust (‐independent) state‐feedback gain but that are not quadratically stabilizable. The proposed analysis, adapted to deal exclusively with output‐feedback, follows the experiment presented in Reference 18, considering 100 systems for each combination of n x ∈ {2, 3} states and N ∈ {2, … , 5} vertices. The case to be addressed is gain‐scheduled (affine dependence on the scheduling parameters) SOF stabilization considering the parameters as time‐varying with arbitrarily fast rates of variation.…”

“…The technique proposed in this article (A1) with is compared with: [44, theorem 2] (PdO); [37, eq. (49)] (dCC) by eliminating the last column and row and considering b = 1 (arbitrarily fast rates of variation); [18, theorem 1] with , (RT); [18, algorithm 1] with and degP=1 (RC) [45, theorem 1] (PCP) with (13 values), with multiaffine dependence on and , and all the other optimization variables with affine dependence on . …”

“…Synthesis conditions for models involving uncertain parameters are naturally expressed in terms of infinite‐dimensional optimization problems, and polynomial approximations 2,3 (also known as relaxations ) associated with the use of slack variables 4,5 are certainly important tools that helped to improve the accuracy of the LMI‐based techniques. When dealing with linear parameter‐varying (LPV) systems, 6,7 a common strategy to improve performance is the synthesis of gain‐scheduled 8‐18 filters or controllers, which tends to provide less conservative results than controllers and filters with fixed gains. On the other hand, scheduled gains require a real‐time reading or estimation of the time‐varying parameters, increasing the implementation and computational costs compared with the robust design.…”

Dynamic controllers for local input‐to‐state stabilization of discrete‐time linear parameter‐varying systems with delay and saturating actuators

“…1,2 As a consequence, the research on the control of LPV systems has been extensively explored and included in various engineering applications in the last decades. 3 Instead of using robust controllers, 4 stability and performance have been pursued through the development of parameter varying controllers, which can be linear 5,6 or rational [7][8][9][10] on the parameter. In all cases, the Lyapunov-based approach is used, which usually leads to convex optimization design methods.…”

A Robust Digital Control of a Gyroscope with an Implicit Derivative Estimator

“…Alternatively, the same state feedback scheme is assumed and the states are estimated using observers (Peaucelle and Ebihara (2014); Gao et al (2017). Lastly, an output feedback control can be designed (Rosa et al (2018)).…”