1,721,109 research outputs found
Robustness analysis for linear dynamical systems with linearly correlated parametric uncertainties
No full textThe authors propose an approach for robust pole location analysis of linear dynamical systems with parametric uncertainties. Linear control systems with characteristic polynomials whose coefficients are affine in a vector of uncertain physical parameters are considered. A design region in complex plane for system pole placement and a nominal parameter vector generating a characteristic polynomial with roots in that region are given. The proposed method allows the computation of maximal domains bounded by linear inequalities and centered at the nominal point in system parameter space, preserving system poles in the given region. The solution of this problem is shown to also solve the problem of testing robot location of a given polytope of polynomials in parameter space. It is proved that for stability problems for continuous-time systems with independent perturbations on polynomial coefficients, this method generates the four extreme Kharitonov polynomial
Robust strict positive realness: new results for interval plant plus controller families
No full textA frequency domain approach is used to derive several robust strict positive realness results for interval plants and interval plant plus controller families of transfer functions. Based on simple frequency domain properties of transfer functions, the approach provides a framework for obtaining new results and constructing easy proofs of several important existing results on robust strict positive realness. The main new result states that the minimum of the real part of the transfer functions belonging to an interval plant controller family is achieved on one of the 32 Kharitonov segments of the interval plant. The argument used in the proof is of wider interest and suggests easy ways of proving that robustness of other different frequency properties of interval plant plus controller families of transfer functions, such as robust stability of H∞-norm computation, can be deduced from a fixed number of segments of transfer functions of the family
On the validity domain of H-infinity controllers under saturation constraints
No full textThe H∞ disturbance rejection problem for a family of linear systems subject to control input constraints is considered. A class of controllers generalizing the standard Riccati equation-based state feedback is proposed and an estimate of their domain of validity is derived. A simple criterion for tuning controller parameters for validity domain maximization and local performance improvement is presented
Conditions for global stability of some classes of nonsymmetric neural networksProceedings of 1994 33rd IEEE Conference on Decision and Control
No full textIn this paper we present new conditions ensuring Global Asymptotic Stability (GAS) of the equilibrium point of neural networks. The results are valid both for symmetric and nonsymmetric interconnection matrices and allow for the consideration of all continuous nondecreasing neuron activation functions. Such functions may be unbounded (but not necessarily subjective), may have infinite intervals with zero slope as in a piece-wise-linear model, or both. The conditions for GAS are based on the concept of Lyapunov Diagonally Stable interconnection matrices and are proved via the Lyapunov direct method. In particular, a class of Lyapunov functions of the generalized Lur'e-Postnikov type is used instead of those currently employed in the literature. Several classes of interconnection matrices of applicative interest are shown to satisfy these conditions
Robust Switching Control: Stability Analysis and Application to Active Disturbance Attenuation
No full textThis note deals with the problem of controlling an uncertain discrete-time linear system by means of a hybrid controller in the form of a linear system whose parameters switch among a finite number of possible configurations, called modes. We suppose that each single controller is designed in order to individually ensure robust stability for a dual-Youla uncertainty model. Then, we show that robust stability of the switching controller can be directly related to robust stability of each single controller mode, in that it is possible to implement the switching controller so that robust stability is guaranteed for any possible switching sequence. This allows one to freely select the switching signal so as to enhance performance, for instance by selecting in real time the control mode displaying the best potential performance with respect to the current operating conditions. An application of the ideas to the problem of active disturbance attenuation is presented and simulation results are shown to validate the proposed solution
Enhancing strict positive realness condition on families of polynomials by filter design
No full textSome results on strict positive realness of families of polynomials are given. The main motivation for these results is the need for design criteria of filters ensuring the convergence of algorithms in the presence of uncertainty in the plant model in the area of identification and adaptive control. Two main results are given. The first provides analytical conditions under which a family of polynomials with zeros in a prescribed region of the complex plane is strict positive real or can be made strict positive real over an assigned region of the complex plane through the use of a suitable filter. The second is a design result providing a parameterization of a family of filters maximizing the region of the complex plane on which strict positive realness is achievable
Synthesis of robust strictly positive real systems with l_2 parametric uncertainty
No full textThe problem of designing filters ensuring strict positive realness of a family of uncertain polynomials over an assigned region of the complex plane is frequently investigated issue in the analysis of absolute stability of nonlinear Lur'e systems and the design of adaptive schemes. This paper addresses the problem of designing a continuous-time rational filter when the uncertain polynomial family is assumed to be an ellipsoid in coefficient space. It is shown that the stability of all the polynomials of such a family is a necessary and sufficient condition for the existence of the filter. More importantly, contrary to the results available for the case of a polyhedral uncertainty set in coefficient space, it turns out that the filter is a proper rational function with degree smaller than twice the degree of the uncertain polynomials. Furthermore, a closed form solution to the filter synthesis problem based on polynomial factorization is derived
Efficient computation of frequency response for systems with interval plants
No full textFrequency domain properties of uncertain rational functions depending on two independent interval polynomials are investigated. Several simplifications for efficient computation of the envelope of the Nyquist plots of the uncertain family are reported. Stronger computational reduction results are given for the Bode magnitude and phase plots of an interval plant-controller family of transfer functions. These results allow for a clear understanding of the extremality properties of several frequency domain performance specifications commonly used in control system design
Vertices and segments of interval plants are not sufficient for step response analysis
No full textInterval plants are of interest in control theory as models of uncertain systems. They are useful because many worst-case analyses of these models are simple to carry out. For example, robust stability of an interval plant can be determined by investigating only the four Kharitonov vertices of the denominator polynomial. Also, the maximum peak of the Bode magnitude plot can be found using just 16 special plant vertices. These 16 vertices are connected by 32 special line segments. Most stability and frequency domain analyses that cannot be done using only the special vertices can be carried out using just the segments. From these results, it is tempting to conjecture that the 16 vertices or at least the 32 segments are adequate for step response analyses. This paper presents examples showing that these conjectures are not true
Input–Output Characterization of the Dynamical Properties of Circuits with a Memelement
Full text linkThe paper proposes a novel input–output approach to characterize the dynamical properties of a class of circuits composed by a linear time-invariant two-terminal element coupled with one of the ideal memelements (memory elements) introduced by Prof. L. O. Chua, i.e. memristors, memcapacitors, and meminductors. The developed approach permits to readily determine the conditions under which the dynamics of any circuit of the class admits a first integral. It is also shown that the circuit dynamics can be obtained by collecting the dynamical behavior displayed by a canonical reduced-order input–output system subject to a constant input of any amplitude. Notably, the reduced-order system exactly describes the dynamics of a circuit forced by a constant generator and with a nonlinear memoryless element in place of the memelement. The relation between the proposed input–output approach and the available state space ones(e.g. Flux-Charge Analysis Method (FCAM)) is also addressed. The main result is that explicit expressions of the invariant manifolds can be directly obtained in the voltage–current state space. Finally, it is shown how the approach also applies to circuits which contain forcing generators. It is believed that the proposed input–output approach can be a useful alternative to state space methods for studying multistability and control issues
- …
