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 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 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.     

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.     

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.     

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.     

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.     

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 sampled-data composite systems with many nonlinearities

A sampled-data composite system given by a set of vector difference equationsx_{i}(tau + 1) - x_{i}(tau) = sum min{j = 1} max{n} A_{ij} f_{j}[x_{j}(tau)], i = 1 ..., nis dealt with. The system given byx_{i}(tau + 1) - x_{i}(tau) = A_{ij} f_{i}[x_{i}(tau)]is referred to as theith isolated subsystem. It is shown that the composite system is asymptotically stable in the large if the fisatisfy certain conditions and the leading principal minors of the determinant|b_{ij}|, i,j = 1, ..., n,are all positive. Here, the diagonal element biiis a positive number such that|x_{i}(tau + 1)| - |x_{i}(tau) | leq - b_{ij}| f_{i}[x_{i}(tau)]|holds with regard to the motion of theith isolated subsystem, and the nondiagonal elementb_{ij} , i neq j, is the minus of|A_{ij}|, which is defined as the maximum of|A_{ij}x_{j}|, for|x_{j}| = 1. Some extensions of this result are also given. Composite relay controlled systems are studied as examples.     

Stability analysis and anti-windup design of switched systems with actuator saturation

The stability analysis and anti-windup design problem is investigated for two linear switched systems with saturating actuators by using the single Lyapunov function approach. Our purpose is to design a switching law and the anti-windup compensation gains such that the maximizing estimation of the domain of attraction is obtained for the closed-loop system in the presence of saturation. Firstly, some sufficient conditions of asymptotic stability are obtained under given anti-windup compensation gains based on the single Lyapunov function method. Then, the anti-windup compensation gains as design variables are presented by solving a convex optimization problem with linear matrix inequality (LMI) constraints. Two numerical examples are given to show the effectiveness of the proposed method.     

Multirate digital filters

This paper provides a review of recent developments in multirate digital filters and attempts to fill a long existing gap between multirate digital filters and multirate sampled-data feedback control systems.