Stability analysis for a class of digital filters with single saturation nonlinearity

In this paper, a new stability criterion for a class of digital filters with single saturation nonlinearity is presented in the form of a linear matrix inequality. Numerical examples are given to show the effectiveness of the obtained results.     

Stability analysis of systems with multiple nonlinearities

This paper shows a method for using describing functions in a control system with multiple nonlinearities. The linear system resulting after the proper describing functions have been inserted is analyzed using an "input dependent root locus" which is a modified root locus technique. The rules for construction of the input dependent locus and a proof of its applicability are given along with examples which illustrate the method. The technique shows the existence of limit cycles, their amplitude and frequency when they exist, and the stability of the limit cycle.     

Stability analysis of a class of digital filters utilizing single saturation nonlinearity

A novel criterion for the global asymptotic stability of a class of digital filters utilizing single saturation nonlinearity is presented. An example showing the effectiveness of the present criterion is given.     

Stability analysis and controller synthesis for discrete linear time-delay systems with state saturation nonlinearities

The problem of global asymptotic stability analysis and controller synthesis for a class of discrete linear time-delay systems with state saturation nonlinearities is investigated. With the introduction of a free matrix whose infinity norm is less than or equal to 1, the state of discrete linear time-delay systems with state saturation is bounded by a convex hull, which makes it feasible to apply a suitable Lyapunov functional to obtain a sufficient condition for global asymptotic stability. It is also shown that this condition can be extended to controller synthesis and discrete time-delay systems with partial state saturation. The obtained results are expressed in terms of matrix inequalities that can be solved by the presented iterative linear matrix inequality approach. The effectiveness of these results is demonstrated by some numerical examples.     

Stability analysis of a class of systems with parameter uncertainties and with state saturation nonlinearities

For linear systems with parameter uncertainties and subject to state saturation, we establish results concerning the global asymptotic stability of an equilibrium. In addition to providing a means for a qualitative analysis, these results also enable us to address the stabilizability of such systems by means of linear state feedback. Systems of the type considered herein capture two important phenomena commonly encountered in the modelling process: (i) system parameter uncertainties (which in the present case are modelled by means of interval matrices), and (ii) operation of systems over a wide range (which in the present case is accounted for by state saturation nonlinearities). We demonstrate the applicability of the present results by means of several specific examples.     

Stability analysis and state feedback stabilization of pendulum-like systems with multiple nonlinearities

This paper addresses the Lagrange stability analysis problem and the state feedback Lagrange stabilization problem for pendulum-like systems with multiple nonlinearities. An existing method for analysing the Lagrange stability of pendulum-like systems with a single nonlinearity is generalized to pendulum-like systems with multiple nonlinearities. Also, a non-degeneracy condition of the existing Lagrange stability criterion is removed and a strict frequency-domain inequality is used instead. To study the state feedback Lagrange stabilization problem, this paper develops an extended strict bounded real lemma for linear systems which are not stable but stabilizable. A sufficient condition for state feedback Lagrange stabilization is proposed in terms of an algebraic Riccati equation with a sign indefinite solution.     

有限字长影响下定点滤波器的稳定性分析

针对飞控软件的精度测试,结合实际研究了有限字长影响下定点数字滤波器的稳定性,分析了乘积舍入与补码溢出对系统的非线性影响,给出系统舍入稳定与溢出稳定的定义,获得了系数量化、乘积舍入以及补码溢出等误差共同影响下有限精度系统舍入稳定且溢出稳定的充分条件。     

Stability analysis for continuous-time systems with actuator saturation

The aim of this paper is to study the determination of the stability regions for continuous-time systems subject to actuator saturation. Using an affine saturation-dependent Lyapunov function, a new method is proposed to obtain the estimation of the domain of attraction of the closed-loop system. A family of linear matrix inequalities （LMIs） that provides sufficient conditions for the existence of this type of Lyapunov function are presented. The results obtained in this paper can reduce the conservativeness compared with the existing ones. Numerical examples are given to illustrate the effectiveness of the proposed results.     

Stability criterion forN-dimensional digital filters

The stability requirement for one-dimensional recursive filters is well known. A stability theorem forn-dimensional recursive filters is proved wherein the denominator of the filter is ann-dimensional power series. A Tauberian theorem due to Wiener yields the desired result in the general case.     

状态饱和离散线性系统的稳定性分析

讨论一类具有状态饱和非线性的离散线性系统稳定性分析问题. 通过引入无穷范数小于等于1 的自由矩阵与对角元素非正的对角矩阵, 将状态饱和离散线性系统的状态变量约束在一个凸多面体内, 进而以矩阵不等式形式给出状态饱和离散线性系统的稳定性判据, 并给出该矩阵不等式的迭代线性矩阵不等式算法. 基于这一稳定性判据, 给出了基于迭代线性矩阵不等式的状态反馈控制律设计算法. 通过状态饱和离散线性系统的状态空间分割方法, 给 出了保守性更小的稳定性判据, 并给出了相应的迭代线性矩阵不等式算法. 数值例子验证了所给出方法的正确性与有效性.

     

Elimination of overflow oscillations in digital filters employing saturation arithmetic

A criterion for the nonexistence of overflow oscillations in a class of digital filters employing saturation arithmetic is presented. The criterion is based on a novel characterization of the saturation nonlinearity (namely, the ‘reduced sector’ characterization) and, hence, is quite distinct from previously reported criteria.     

An improved criterion for the global asymptotic stability of fixed-point state-space digital filters with saturation arithmetic

A criterion for the global asymptotic stability of fixed-point state-space digital filters with saturation arithmetic is presented. The criterion makes use of the structural properties of the multiple saturation nonlinearities in greater detail than several existing criteria. The relationship between the presented criterion and some existing ones is established. Through the relationship, it is clear that the presented criterion is less conservative than corresponding existing results, which is confirmed by a numerical example.     

A new stability analysis and controller design method for discrete-time linear systems with saturation nonlinearities

The problems of stability analysis and controllers design for discrete-time linear systems subject to state saturation nonlinearities are investigated in this paper. Both full state saturation and partial state saturation are considered. It is well known to all that the controller design problem under state saturation is very difficult and complex to deal with. In order to overcome the difficulty, a new and tractable system is constructed, and it can be proved that the constructed system is with the same domain of attraction as the original system. With the aid of this property, to estimate the domain of attraction of the original system, an LMI-based method is presented for estimating the domain of attraction of the origin for the new constructed system under state saturation. Further, two optimization algorithms are developed for constructing dynamic output-feedback controllers and state feedback controllers, respectively, which guarantee that the domain of attraction of the origin for the closed-loop system is as ’large’ as possible. An example is provided to demonstrate the effectiveness of the new method.     

Asymptotic stability of continuous-time systems with saturation nonlinearities

A new criterion is established for global asymptotic stability of second-order systems modeled by equations of the type , where σ is the saturation function. The derivation is based on the Bendixon's theorem on limit cycles and a closer study of the trajectories of the systems. Applications to stabilization of more general cascade nonlinear systems are also discussed.     

Elimination of overflow oscillations in direct form digital filters using saturation arithmetic

A novel frequency-domain criterion for the elimination of limit cycles in a class of digital filters using saturation arithmetic is presented. An example showing the effectiveness of the present criterion is given.     

H∞ control for linear systems with state saturation nonlinearities

The problem of H_∞ control for a class of linear systems with state saturation nonlinearities is considered in this paper. By introducing a row diagonally dominant matrix with negative diagonal elements and a diagonal matrix with positive elements, the H_∞ control problem is reduced to a matrix inequality feasibility problem that can be solved by the proposed iterative linear matrix inequality algorithm. The effectiveness of the presented method is demonstrated by a numerical example. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability of uncertain systems with hysteresis nonlinearities

Stability of systems with hysteresis nonlinearities, parametric uncertainty and finite dimensional unmodelled dynamics is considered. Conditions for exponential decay of the signals in the system to an equilibrium position are given. The equilibrium is generally not unique. The stability condition is given in terms of a frequency domain inequality, which involves the transfer function of the nominal system and a multiplier, The search for a suitable multiplier can be performed by use of convex optimization in terms of linear matrix inequalities. A simple example is given that illustrates our result. © 1998 John Wiley & Sons, Ltd.     

Output error convergence of adaptive filters with compensation foroutput nonlinearities

Output error convergence of a Wiener model-based nonlinear stochastic gradient algorithm is analyzed. The normalized scheme estimates the parameters of a linear finite impulse response model in cascade with a known output nonlinearity. The algorithm can be interpreted as a normalized least mean square algorithm with compensation for an output nonlinearity. Linearizing inversion of the nonlinearity is not utilized. Global output error convergence is then proved, provided that the nonlinearity is monotone (not strictly monotone), and provided that a previously observed mechanism resulting in deadlock does not occur. The algorithm and the analysis include important practical cases like sensor saturation and dead zones that must be excluded when global parametric convergence is studied     

Stability of systems with several monotone nonlinearities

This paper is devoted to stability problems of automatic control systems. Frequency domain criteria for global asymptotic stability of equilibrium sets for new classes of nonlinearities are derived. Results are illustrated by examples.