An adaptive output feedback controller for single input feedback linearizable systems is proposed. The output derivatives are estimated with a state high-gain observer, and the matched uncertainties are handled using a modelling error compensation method. Compared with existing adaptive methods, this approach avoids overparameterizations yielding an (n+1)-order compensator, where n is the system dimension. Semiglobal stability is proven with the aid of existing results on the stability of controlled nonlinear systems with high-gain state observation. Copyright © 1999 John Wiley & Sons, Ltd.

Adaptive control of feedback linearizable systems: a modelling error compensation approach

On the stability properties of linear dynamic time-varying unforced systems involving switches between parameterizations from topologic considerations via graph theory

This paper firstly considers the exponential stability of unforced linear systems of slowly time-varying dynamics. Possible switchings of the system structure to unstable dynamics during certain finite time intervals are admitted. The maintenance of global exponential stability does not necessarily require at most a finite number of switchings in the dynamics while infinitely many switches can also lead to stability. The mechanism to achieve stability under infinitely many switches in the dynamics is to maintain the system in the stable region during time intervals of sufficiently large length without switches provided that the system dynamics evolves at a sufficiently small rate with time. Special attention is paid to the robust tolerance to a class of state disturbances and to the case of a time-varying matrix of dynamics that possess either piecewise constant or constant eigenvalues. The obtained results can be relevant for their use in stability issues for the cases of multimodel non-adaptive and adaptive control with improved transient performances.

Robust stability of a class of linear time‐varying systems

Many chemical processes can be modeled for the purpose of feedback controller tuning by a first-order process. In this case, PI feedback controllers are mostly used to regulate the process. Due to the capabilities of the integral action to estimate load disturbance, a certain stability margin in the closed-loop system is obtained. That is, the integral variable provides an estimate of the load disturbance, which is counteracted in the feedback loop. The aim of the work is to derive a model-based PI feedback controller with extended capabilities to estimate dynamic disturbances (PII2 feedback controller). It is shown that, under certain gain choices, the proposed controller reduces to a classical PI one. The performance of the controller is illustrated via numerical simulations of two chemical processes.

A PI Controller with Disturbance Estimation

Robust stability of a class of linear time-varying systems

This paper investigates the robustness of time-varying linear systems under a large class of complex time-varying perturbations. Previous results8 which were restricted to bounded linear perturbations of output feedback type are generalized to unbounded and nonlinear perturbations of multi-output feedback type. We establish a lower bound for the stability radius of these systems and show how it may be possible to improve the bound using time-varying scalar transformations of the state, input and output variables. The results are applied to derive Gershgorin type stability criteria for time-varying linear systems.

A. J. Pritchard

Papers

Robust exponential stability of time-varying linear systems