3,708 research outputs found
Model Reduction of Multi-Dimensional and Uncertain Systems
We present model reduction methods with guaranteed error bounds for systems represented by a Linear Fractional Transformation (LFT) on a repeated scalar uncertainty structure. These reduction methods can be interpreted either as doing state order reduction for multi-dimensionalsystems, or as uncertainty simplification in the case of uncertain systems, and are based on finding solutions to a pair of Linear Matrix Inequalities (LMIs). A related necessary and sufficient condition for the exact reducibility of stable uncertain systems is also presented
Dissipative stability theory for linear repetitive processes with application in iterative learning control
This paper develops a new set of necessary and sufficient conditions for the stability of linear repetitive processes, based on a dissipative setting for analysis. These conditions reduce the problem of determining whether a linear repetitive process is stable or not to that of checking for the existence of a solution to a set of linear matrix inequalities (LMIs). Testing the resulting conditions only requires compu- tations with matrices whose entries are constant in comparison to alternatives where frequency response computations are required
LMI approach to mixed performance objective controllers: application to Robust â2 Synthesis
The problem of synthesizing a controller for plants subject to arbitrary, finite energy disturbances and white noise disturbances via Linear Matrix Inequalities (LMIs) is presented. This is achieved by considering white noise disturbances as belonging to a constrained set in â2. In the case of where only white noise disturbances are present, the procedure reduces to standard â2 synthesis. When arbitrary, finite energy disturbances are also present, the procedure may be used to synthesize general mixed performance objective controllers, and for certain cases, Robust â2 controllers
Positive trigonometric polynomials for strong stability of difference equations
We follow a polynomial approach to analyse strong stability of linear
difference equations with rationally independent delays. Upon application of
the Hermite stability criterion on the discrete-time homogeneous characteristic
polynomial, assessing strong stability amounts to deciding positive
definiteness of a multivariate trigonometric polynomial matrix. This latter
problem is addressed with a converging hierarchy of linear matrix inequalities
(LMIs). Numerical experiments indicate that certificates of strong stability
can be obtained at a reasonable computational cost for state dimension and
number of delays not exceeding 4 or 5
Co-design of output feedback laws and event-triggering conditions for linear systems
We present a procedure to simultaneously design the output feedback law and
the event-triggering condition to stabilize linear systems. The closed-loop
system is shown to satisfy a global asymptotic stability property and the
existence of a strictly positive minimum amount of time between two
transmissions is guaranteed. The event-triggered controller is obtained by
solving linear matrix inequalities (LMIs). We then exploit the flexibility of
the method to maximize the guaranteed minimum amount of time between two
transmissions. Finally, we provide a (heuristic) method to reduce the amount of
transmissions, which is supported by numerical simulations
Linearly Convergent First-Order Algorithms for Semi-definite Programming
In this paper, we consider two formulations for Linear Matrix Inequalities
(LMIs) under Slater type constraint qualification assumption, namely, SDP
smooth and non-smooth formulations. We also propose two first-order linearly
convergent algorithms for solving these formulations. Moreover, we introduce a
bundle-level method which converges linearly uniformly for both smooth and
non-smooth problems and does not require any smoothness information. The
convergence properties of these algorithms are also discussed. Finally, we
consider a special case of LMIs, linear system of inequalities, and show that a
linearly convergent algorithm can be obtained under a weaker assumption
Almost sure exponential stabilisation of stochastic systems by state-feedback control
So far, a major part of the literature on the stabilisation issues of stochastic systems has been dedicated to mean square stability. This paper develops a new class of criteria for designing a controller to stabilise a stochastic system almost surely which is unable to be stabilised in mean-square sense. The results are expressed in terms of linear matrix inequalities (LMIs) which are easy to be checked in practice by using MATLAB Toolbox. Moreover, the control structure in this paper appears not only in the drift part but also in the diusion part of the underlying stochastic system
Delay-dependent robust stability of stochastic delay systems with Markovian switching
In recent years, stability of hybrid stochastic delay systems, one of the important issues in the study of stochastic systems, has received considerable attention. However, the existing results do not deal with the structure of the diffusion but estimate its upper bound, which induces conservatism. This paper studies delay-dependent robust stability of hybrid stochastic delay systems. A delay-dependent criterion for robust exponential stability of hybrid stochastic delay systems is presented in terms of linear matrix inequalities (LMIs), which exploits the structure of the diffusion. Numerical examples are given to verify the effectiveness and less conservativeness of the proposed method
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