Observer-based robust stabilization for a class of uncertain polynomial systems

Abstract

This paper focuses on the observer-based robust stabilization problem for a class of polynomial systems with norm-bounded time-varying uncertainties. The structural features of such systems guarantee the fulfilment of the separation principle between the reduced-order observer and the state feedback. The existence conditions of the observer-based robust stabilization controller are obtained by using Lyapunov stability theory. Furthermore, based on the polynomial sum of squares (SOS) theory, the above conditions are transformed into the corresponding SOS convex optimization constraints, for the avoidance of computing difficulties that exist widely in the control of non-linear systems. Finally, two numerical examples are given to illustrate the feasibility and effectiveness of the proposed approach.

Robust nonlinear H∞ output-feedback control for flexible spacecraft attitude manoeuvring

“…Lemma 1: (Zhou and Zeng, 2017b). Suppose B R ⊂ R n is a bounded and closed subset, Φ 1 ( x ) ∈ R ( x ) p × p and Φ 2 ( x ) ∈ R ( x ) q × q are continuous polynomial matrices in x ∈ B R , then Φ 1 ( x ) < 0 and Φ 2 ( x ) < 0 if and only if for any given continuous polynomial matrix Φ 3 ( x ) ∈ R ( x …”

“…we construct the following state-observer by using the input and output signals u and y to estimate the flexible modes (Zhou and Zeng, 2017b).…”

Observer‐based controller synthesis for uncertain polynomial systems

“…Due to the effectiveness of the polynomial system in modelling the non-linear system, there are a large number of studies, recently, paying attention to design the observer and controller for the polynomial systems [5,6,[8][9][10][11][12][13][14][15][16]. For example, an observer was designed for the polynomial system to estimate the states asymptotically and eliminate the impact of unknown inputs [5].…”

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

“…The TS fuzzy models are described by fuzzy blending of some local subsystems (Song et al, 2016). Depending on the consequent part of the fuzzy IF-THEN rules, the TS fuzzy model is called a linear (Zhang et al, 2016), ane (Beyhan, 2017; Wang et al, 2016), bilinear (Chang and Hsu, 2016; Hamdy and Hamdan, 2015) and polynomial (Mardani et al, 2017b; Vafamand et al, 2017b; Zhou and Zeng, 2017) fuzzy model. The simplicity of the TS-based fuzzy control makes this method a very intresting research field (Khooban et al, 2016).…”

“…Originally, the parallel distributed compensation (PDC) and non-PDC schemes were widely employed for the linear TS fuzzy systems through linear matrix (LMI) techniques (Chang et al, 2012; Dong and Yang, 2017; Mardani et al, 2017a). Recently, polynomial (Mardani et al, 2017b; Vafamand et al, 2017b; Zhou and Zeng, 2017) and polynomial fuzzy (Pitarch et al, 2017) controllers have attracted lots of attention to deal with the polynomial and polynomial fuzzy models. Based on the polynomial fuzzy model approach, sufficient stability conditions are derived in terms of sum-ofsquares (SOS) decomposition conditions (Tanaka et al, 2016).…”