J. E. Gibson

Bio: J. E. Gibson is an academic researcher from Purdue University. The author has contributed to research in topics: Exponential stability & Describing function. The author has an hindex of 2, co-authored 2 publications receiving 61 citations.

On the Asymptotic Stability of a Class of Saturating Sampled-Data Systems

Abstract: This paper presents an extension of the Lur'e stability function to a class of discrete-time systems which may contain saturation-type nonlinear elements. Examples are presented which demonstrate the improved stability inequalities available from this function.

A New Dual-Input Describing Function and an Application to the Stability of Forced Nonlinear Systems

Abstract: A new general DIDF (dual input describing function) has been analytically derived for single-valued nonlinearities subjected to two arbitrary noncommensurate sine waves. The development corroborates a previous approximate development for two sine waves widely separated in frequency. The new DIDF is applied to the problem of the stability of nonlinear systems subjected to sinusoidal forcing. It is shown that the conventional DF (describing function) cannot be used for nonautonomous systems without additional safeguards. After it has been shown by the DIDF that no auto-oscillations exist for given input conditions it is proper to employ the conventional DF in any of the methods suggested in the literature to obtain the closed-loop frequency response under those conditions.

Explicit construction of quadratic lyapunov functions for the small gain, positivity, circle, and popov theorems and their application to robust stability. part II: Discrete-time theory

Abstract: The purpose of this paper is to construct Lyapunov functions to prove the key fundamental results of linear system theory, namely, the small gain (bounded real), positivity (positive real), circle, and Popov theorems. For each result a suitable Riccati-like matrix equation is used to explicitly construct a Lyapunov function that guarantees asymptotic stability of the feedback interconnection of a linear time-invariant system and a memoryless nonlinearity. Lyapunov functions for the small gain and positivity results are also constructed for the interconnection of two transfer functions. A multivariable version of the circle criterion, which yields the bounded real and positive real results as limiting cases, is also derived. For a multivariable extension of the Popov criterion, a Lure-Postnikov Lyapunov function involving both a quadratic term and an integral of the nonlinearity, is constructed. Each result is specialized to the case of linear uncertainty for the problem of robust stability. In the case of the Popov criterion, the Lyapunov function is a parameter-dependent quadratic Lyapunov function.

Impact of distributed gate resistance on the performance of MOS devices

Abstract: This paper describes the impact of gate resistance on cut-off frequency (f/sub T/), maximum frequency of oscillation (f/sub max/), thermal noise, and time response of wide MOS devices with deep submicron channel lengths. The value of f/sub T/ is proven to be independent of gate resistance even for distributed structures. An exact relation for f/sub max/ is derived and it is shown that, to predict f/sub max/, thermal noise, and time response, the distributed gate resistance can be divided by a factor of 3 and lumped into a single resistor in series with the gate terminal. >

Explicit construction of quadratic Lyapunov functions for the small gain, positivity, circle and Popov theorems and their application to robust stability

Abstract: Lyapunov function proofs of sufficient conditions for asymptotic stability are given for feedback interconnections of bounded real and positive real transfer functions. Two cases are considered: a proper bounded real (resp., positive real) transfer function with a bounded real (resp., positive real) time-varying memoryless nonlinearity; and two strictly proper bounded real (resp., positive real) transfer functions. A similar treatment is given for the circle and Popov theorems. Application of these results to robust stability with time-varying bounded real, positive real, and sector-bounded uncertainty is discussed. >

The status of stability theory for deterministic systems

Abstract: This paper attempts to summarize and place in perspective some of the recent contributions to stability theory. The major emphasis is on work which relates closely to applications in control, circuit theory, and aerospace systems. The frequency domain stability criteria for nonlinear and time-varying feedback loops are discussed in some detail. A large number of references describing both theoretical developments and applications are included.