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A Lyapunov Functional for the Cubic Nonlinearity Activator-Inhibitor Model Equation
(1998)
The cubic nonlinearity activator-inhibitor model equation is a simpleexample of a pattern-forming system for which strong mathematical resultscan be obtained. Basic properties of solutions and the derivation ofa Lyapunov ...
Guardian Maps and the Generalized Stability of Parametrized Families of Matrices and Polynomials
(1988)
The generalized stability of families of real matrices and polynomials is considered. (Generalized stability is meant in the usual sense of confinementof matrix eigenvalues or polynomial zeros to a prespecified domain in ...
Non-Smooth Robust Stabilization of a Family of Linear Systems in the Plane
(1996)
In this paper, we use merely continuous feedback to robustly stabilize a class of parameterized family of linear systems in the plane. We introduce a new interpolation method that enables us to construct a robust stabilizer ...
Closed-Loop Monitoring Systems for Detecting Incipient Instability
(1998)
Monitoring systems are proposed for the detection of incipientinstability in uncertain nonlinear systems. The work employsgeneric features associated with the response to noise inputsof systems bordering on instability. ...
On Participation Factors for Linear Systems
(1999)
Participation factors are nondimensional scalars that measure the interaction betweenthe modes and the state variables of a linear system. Since their introduction byVerghese, P'erez-Arriaga and Schweppe, participationfactors ...
Analysis of a complex activator-inhibitor equation
(1999)
Basic properties of solutions and a Lyapunov functionalare presented for a complex activator-inhibitor equation witha cubic nonlinearity.Potential applications include control of coupled-oscillator arrays(for quasi-optical ...
Control of Large Actuator Arrays Using Pattern-Forming Systems
(1998)
Pattern-forming systems are used to model many diverse phenomena from biology,chemistry and physics. These systems of differential equations havethe property that as a bifurcation (or control) parameter passes through ...
Absolute Stability Theory, Theory, and State-Space Verification of Frequency-Domain Conditions: Connections and Implications for Computation
(1997)
The main contribution of the paper is to show the equivalence between the following two approaches for obtaining sufficient conditions for the robust stability of systems with structured uncertainties: (i) apply the classical ...
Time-Varying Simultaneous stabilization, Part I. Countable families of LTI systems
(1996)
In this paper, we introduce a new method that enables us to prove that given any finite family of LTI (linear time-invariant) systems, there exists a continuous time varying feedback law that simultaneously globally ...
Time-Varying simultaneous stabilization, Part II. Finite families of nonlinear systems
(1996)
In this paper, we derive sufficient conditions for the existence of a continuous time-varying feedback law that simultaneously locally or globally asymptotically stabilizes a finite family of nonlinear systems. We then ...