Quadratic stabilizability of uncertain linear systems containing both constant and time-varying uncertain parameters

1988 ◽  
Vol 57 (3) ◽  
pp. 439-461 ◽  
Author(s):  
I. R. Petersen
Keyword(s):  
Linear Systems ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Uncertain Linear Systems

scholarly journals Transformation of Uncertain Linear Systems with Real Eigenvalues into Cooperative Form: The Case of Constant and Time-Varying Bounded Parameters

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 85
Author(s):  
Andreas Rauh ◽  
Julia Kersten
Keyword(s):  
Linear Systems ◽  
Initial Conditions ◽  
A Priori ◽  
Real Life ◽  
Reachability Analysis ◽  
Interval Methods ◽  
Space Representation ◽  
Uncertain Parameters ◽  
Time Varying ◽  
Similarity Transformations

Continuous-time linear systems with uncertain parameters are widely used for modeling real-life processes. The uncertain parameters, contained in the system and input matrices, can be constant or time-varying. In the latter case, they may represent state dependencies of these matrices. Assuming bounded uncertainties, interval methods become applicable for a verified reachability analysis, for feasibility analysis of feedback controllers, or for the design of robust set-valued state estimators. The evaluation of these system models becomes computationally efficient after a transformation into a cooperative state-space representation, where the dynamics satisfy certain monotonicity properties with respect to the initial conditions. To obtain such representations, similarity transformations are required which are not trivial to find for sufficiently wide a-priori bounds of the uncertain parameters. This paper deals with the derivation and algorithmic comparison of two different transformation techniques for which their applicability to processes with constant and time-varying parameters has to be distinguished. An interval-based reachability analysis of the states of a simple electric step-down converter concludes this paper.

scholarly journals An observer-based control of linear systems with uncertain parameters

2016 ◽  
Vol 26 (4) ◽  
pp. 565-576 ◽  
Author(s):  
Mostafa Rachik ◽  
Mustapha Lhous
Keyword(s):  
Linear Systems ◽  
Uncertain Parameters ◽  
Reduced Order ◽  
Numerical Examples ◽  
Reduced Order Observer ◽  
Control Of Linear Systems ◽  
Uncertain Linear Systems

Abstract In this paper, the observer-based control for a class of uncertain linear systems is considered. Exponential stabilizability for the system is studied and reduced-order observer is discussed. Numerical examples are given to illustrate obtained results.

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