Mathematics of Control, Signals and Systems
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Elimination in control theory
Mathematics of Control, Signals and Systems - Tập 4 - Trang 17-32 - 1991
For nonlinear systems described by algebraic differential equations (in terms of “state” or “latent” variables) we examine the converse to realization,elimination, which consists of deriving an externally equivalent representation not containing the state variables. The elimination in general yields not only differential equations but also differentialinequations. We show that the application of d...... hiện toàn bộ
Spectral properties of pseudo-resolvents under structured perturbations
Mathematics of Control, Signals and Systems - - 2009
Remarks on input-to-state stability of collocated systems with saturated feedback
Mathematics of Control, Signals and Systems - Tập 32 - Trang 293-307 - 2020
We investigate input-to-state stability (ISS) of infinite-dimensional collocated control systems subject to saturated feedback. Here, the unsaturated closed loop is dissipative and uniformly globally asymptotically stable. Under an additional assumption on the linear system, we show ISS for the saturated one. We discuss the sharpness of the conditions in light of existing results in the literature...... hiện toàn bộ
Rational approximations of spectral densities based on the Alpha divergence
Mathematics of Control, Signals and Systems - Tập 26 - Trang 259-278 - 2013
We approximate a given rational spectral density by one that is consistent with prescribed second-order statistics. Such an approximation is obtained by selecting the spectral density having minimum “distance” from under the constraint corresponding to imposing the given second-order statistics. We analyze the structure of the optimal solutions as the minimized “distance” varies in the Alpha diver...... hiện toàn bộ
Limits of generalized state space systems under proportional and derivative feedback
Mathematics of Control, Signals and Systems - Tập 10 - Trang 97-124 - 1997
In this paper we study the high-gain feedback classification problem for generalized state space systems. We solve this problem for proportional and derivative feedback transformations of regularizable systems, i.e., we give necessary and sufficient conditions for a regularizable system to be a limit of a given system under high-gain proportional and derivative feedback. We also derive a new compl...... hiện toàn bộ
Convergence analysis of central and minimax algorithms in scalar regressor models
Mathematics of Control, Signals and Systems - Tập 18 - Trang 66-99 - 2005
In this paper, the estimation of a scalar parameter is considered with given lower and upper bounds of the scalar regressor. We derive non-asymptotic, lower and upper bounds on the convergence rates of the parameter estimate variances of the central and the minimax algorithms for noise probability density functions characterized by a thin tail distribution. This presents an extension of the previo...... hiện toàn bộ
Symmetries of differential behaviors and finite group actions on free modules over a polynomial ring
Mathematics of Control, Signals and Systems - Tập 6 Số 4 - Trang 307-321 - 1993
In this paper we study finite group symmetries of differential behaviors (i.e., kernels of linear constant coefficient partial differential operators). They lead us to study the actions of a finite group on free modules over a polynomial ring. We establish algebraic results which are then used to obtain canonical differential representations of symmetric differential behaviors.
The time-varying gap and coprime factor perturbations
Mathematics of Control, Signals and Systems - Tập 8 - Trang 352-374 - 1995
The connection between the time-varying gap metric and two-block problems is utilized to obtain criteria for robust stabilization of linear, discretetime, time-varying systems. In particular we give a formula for the optimal minimal angle for a stabilizable linear time-varying system and show that it has a maximally stabilizing controller.
The singular zero-sum differential game with stability usingH ∞ control theory
Mathematics of Control, Signals and Systems - Tập 4 - Trang 121-138 - 1991
In this paper we consider the zero-sum, infinite-horizon, linear quadratic differential game. We derive sufficient conditions for the existence of (almost) equilibria as well as necessary conditions. Contrary to all classical references we allow for singular weighting on the minimizing player in the cost criterion. It turns out that this problem has a strong relation with the singularH
...... hiện toàn bộ
Lyapunov functions for time-varying systems satisfying generalized conditions of Matrosov theorem
Mathematics of Control, Signals and Systems - Tập 19 - Trang 151-182 - 2007
The classical Matrosov theorem concludes uniform asymptotic stability of time-varying systems via a weak Lyapunov function (positive definite, decrescent, with negative semi-definite derivative along solutions) and another auxiliary function with derivative that is strictly nonzero where the derivative of the Lyapunov function is zero (Mastrosov in J Appl Math Mech 26:1337–1353, 1962). Recently, s...... hiện toàn bộ
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