Exponential stabilisation of nonlinear parameter-varying systems with applications to conversion flight control of a tilt rotor aircraft

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Summary In this paper, the domain of attraction (DA) and the local stabilization problem are investigated under the nonlinear parameter‐varying (NPV) framework. Specifically, to take into account the time‐varying parameter, we generalize the definition of robust DA (RDA) and propose the concept of parameter‐dependent DA (PDA) for NPV systems, together with the sum‐of‐squares (SOS) conditions for their estimations. Differently from the existing DA‐related works, the theoretical results in this paper can be applied to a large class of nonlinear polynomial systems including the time‐invariant, the parameter‐dependent, and the uncertain ones. Moreover, the commonly used iterative/coordinate‐wise search is avoided because we eliminate the bilinear product terms between the Lyapunov functional and the SOS multipliers. We also consider the local stabilization problem of NPV systems, in which the RDA can be specified as a control performance index. Finally, several examples are given for illustration purposes.

Section: Local Stability Analysis Of Npv Systemsmentioning

confidence: 99%

Section: Estimate Of Parameter-dependent Domain Of Attractionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the domain of attraction and local stabilization of nonlinear parameter‐varying systems

Zeng

et al. 2019

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“…In other words, we have to simultaneously deal with nonlinearities and the time‐varying nature of the system. Fortunately, as mentioned in Fu et al, the SOS framework has a favorable “accommodation” property that facilitates constructing polynomial matrices to absorb not only states but also parameters (eg, for u = L (·) P −1 (·) x , the matrix L (·) can be designed as a polynomial one in x , σ ( t ), and

\overset{σ}{true} false(t false)

), provided that these variables are online‐detectable. Therefore, both the states and the parameters can be defined as free variables in the coding of an SOS program, within the environment of Matlab toolbox SOSTOOLS .…”

Section: State Feedback Synthesismentioning

confidence: 99%

“…Essentially, many practical NTV systems can be formulated in a state‐and‐parameter‐dependent linear‐like form as

\begin{matrix} center \\ array \dot{x} = A (x, σ (t)) x + B_{1} (x, σ (t)) ω + B_{2} (x, σ (t)) u \\ array z = C (x, σ (t)) x + D_{11} (x, σ (t)) ω + D_{12} (x, σ (t)) u \end{matrix}

, in which the nonlinearities and time‐varying nature are represented by the dependence of system matrices on the system state and the parameter, respectively, (hereinafter, we will refer it as a nonlinear parameter‐varying (NPV) system). In Fu et al, the concept of NPV systems was first presented, and the exponential stabilization problem of polynomial NPV systems was investigated by using sum‐of‐squares (SOS) convex programming …”

Section: Introductionmentioning

confidence: 99%

H_∞ mixed stabilization of nonlinear parameter‐varying systems

Zeng

Duan

2018

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Summary This paper generalizes the existing finite‐time stability (FTS) analysis/synthesis research to nonlinear time‐varying systems in the nonlinear parameter‐varying (NPV) framework. Specifically, to guarantee both the transient and steady‐state performances for NPV systems with external disturbance and input constraints, concepts of mixed stability and mixed stability with H∞ disturbance attenuation are proposed, together with the corresponding analysis and synthesis methods. Differently from the existing FTS‐related works, the mixed stability in this paper consists of properties of uniform exponential stability in addition to FTS. Existence conditions for an nonlinear time‐varying controller to render an NPV system mixed stable with H∞ disturbance attenuation are given in terms of state‐and‐parameter–dependent linear matrix inequalities. The generalized S‐procedure is used to convexify the input constraints such that the resulting closed‐loop system satisfies the input constraints for any state starting from an admissible set. For the case that both parameters and state are subject to restricted regions, local synthesis results are also provided. All the conditions are in the form of state‐and‐parameter–dependent linear matrix inequalities, which can be efficiently solved by using sum‐of‐squares programming. A simulation example validates the effectiveness of the proposed approach.

Further studies on state estimation of discrete‐time nonlinear parameter varying systems based on a new multiinstant switching observer

Zhou

Xie

Yue

et al. 2020

This article is concerned with further studies on state estimation of discrete-time nonlinear parameter varying systems with the help of an efficient multiinstant switching observer. First, a pair of variable weights for different sampling instants are introduced and thus more featured switching modes for the applied observer are produced by updating and utilizing all the varying elements that vary upon time. Second, an individual designing condition of the developed multiinstant switching observer for each switching mode is derived by considering the specific information of the updated varying elements, respectively. Indeed, the whole obtained result is less conservative than the previous ones. Finally, some comparative simulations are provided in order to illustrate the advantage and benefit of the developed results.