Conference Paper
Controllability and observability of uncertain systems: A robust measure
Dept. of Control & Dynamical Syst., California Inst. of Technol., Pasadena, CA, USA
DOI: 10.1109/CDC.2009.5399774 Conference: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on Source: IEEE Xplore
 Citations (21)
 Cited In (0)

Article: Robust Stability of LTI Systems Over Semialgebraic Sets Using SumofSquares Matrix Polynomials
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ABSTRACT: This paper deals with the robust stability of discretetime linear timeinvariant systems with parametric uncertainties belonging to a semialgebraic set. It is asserted that the robust stability of any system over any semialgebraic set (satisfying a mild condition) is equivalent to solvability of a semidefinite programming (SDP) problem, which can be handled using the available software tools. The particular case of a semialgebraic set associated with a polytope is then investigated, and a computationally appealing method is proposed to attain the SDP problem by means of a sampling technique, introduced recently in the literature. Furthermore, it is shown that the current result encompasses the ones presented in some of the recent works. The efficacy of the proposed method is demonstrated through some illustrative examples, and the results are compared to some of the existing methods.IEEE Transactions on Automatic Control 03/2008; · 2.72 Impact Factor  [Show abstract] [Hide abstract]
ABSTRACT: The robust stability of uncertain linear systems in polytopic domains is investigated in this paper. The main contribution is to provide a systematic procedure for generating sufficient robust stability linear matrix inequality conditions based on homogeneous polynomially parameterdependent Lyapunov matrix functions of arbitrary degree on the uncertain parameters. The conditions exploit the positivity of the uncertain parameters, being constructed in such a way that: as the degree of the polynomial increases, the number of linear matrix inequalities and free variables increases and the test becomes less conservative; if a feasible solution exists for a certain degree, the conditions will also be verified for larger degrees. For any given degree, the feasibility of a set of linear matrix inequalities defined at the vertices of the polytope assures the robust stability. Both continuous and discretetime uncertain systems are addressed, as illustrated by numerical examples.Systems & Control Letters. 01/2006; 55:5261.  [Show abstract] [Hide abstract]
ABSTRACT: In previous works we have proposed a robust stability condition for linear timeinvariant discretetime systems which makes use of a Lyapunov function with linear dependence on the uncertain parameters. This condition is expressed as a set of linear matrix inequalities (LMI) where an additional variable is kept common to all LMI. These features have enabled the development of successful robust filtering and control algorithms. In this short note we investigate possible extensions of this stability condition to handle Lyapunov functions with arbitrary parameter dependence while keeping a variable common to all LMI. By showing that feasibility of the original condition is indeed necessary for the existence of a family of robust stability conditions where the Lyapunov function can have arbitrary dependence on the uncertain parameters, we conclude that no such extensions are possible.Systems & Control Letters 11/2005; 54(11):1131–1134. · 1.67 Impact Factor
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