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This paper studies the problem of the minimum mean squared error estimator for non-parametric nonlinear system identification. It is shown that for a wide class of nonlinear systems, the local linear estimator is a linear (in outputs) asymptotic minimum mean squared error estimator. The class of the systems allowed is characterized by a stability condition that is related to many well studied stability...
Finite-time stability (FTS) requires that the state of a system does not exceed a certain bound during a specified time interval for given bound on the initial state. The concept of FTS introduced exogenous inputs is called finite time boundedness (FTB). This paper gives necessary and sufficient conditions for FTB of linear time-varying continuous-time systems. The conditions are extensions of existing...
This paper proposes novel stability conditions of nonlinear systems in Takagi-Sugeno's form. This problem has been studied over twenty years with many sufficient conditions. Recently, asymptotically necessary and sufficient conditions are obtained, which are preferred with respect to common quadratic Lyapunov function. This paper considers general forms of homogeneously polynomially nonquadratic Lyapunov...
A result originally reported in [3] for linear time invariant single input-single output systems and concerning an invariant and a canonical form of the transfer function matrix of the closed loop system under dynamic feedback compensation is generalized for LTI multivariable systems. This result leads to a characterization of the class of closed loop transfer function matrices which are obtainable...
Motivated by the adaptive control problem for systems with hysteresis, a two-time-scale averaging framework is presented in this paper for systems involving operators, by extending the work of Teel and co-workers. The developed averaging theory is applied to the analysis of a model reference adaptive inverse control scheme for a system consisting of linear dynamics preceded by a Prandtl-Ishlinkskii...
Semi-invariants can be used to study the trajectories of dynamical systems, and, in particular, to study the stability of the origin. The computation of semi-invariants can be based on orbital symmetries, which, in general, are hard to compute even for planar systems. The goal of this paper is to describe several classes of planar systems for which an orbital symmetries can be computed, and to illustrate...
Practical problems require the synthesis of a set of stabilizing controllers that guarantee transient performance specifications such as a bound on the overshoot of its closed loop step response. A majority of these specifications for linear time invariant (LTI) systems can be converted to the requirement of synthesizing a set of stabilizing controllers guaranteeing the non-negative impulse response...
This paper is devoted to the construction of dynamical systems that converge to principal subspaces of multi-set canonical variates using root objective functions. With some modifications, these systems may be converted to new ones that converge to the actual canonical variates. The main important features of two algorithms that have been tested are that the first algorithm converges to the canonical...
Minimum phase systems are the only systems that allow (in disturbance-free unconstrained case) the achievement of perfect tracking in presence of arbitrary reference signals. The question is whether this still holds when the control input is subject to input saturation constraint. Surprisingly, most works on global output tracking in presence of input saturation focused on nonminimum phase systems...
Numerically tractable conditions for input-to-state stability (ISS) analysis are given for a class of nonlinear systems. These conditions originate from ISS inequalities for the cascade connection of the systems and the feedback interconnected system. If class of the systems is restricted such as polynomial ones, then it is possible to avail recent developed sum of squares relaxation of positive polynomials...
In this paper we propose a fixed-order controller design method with frequency domain specifications via generalized KYP lemma. The specifications are given on sensitivity function, complementary sensitivity function, and gain/phase margin. Both the numerator and the denominator of the controller satisfying these constraints can be obtained simultaneously. A closed-loop stability condition is given...
A constructive procedure for robust output controller design is given starting from the unit hypercube of reflection coefficients of monic polynomials. This procedure consists of two main steps: convex approximation of the stability domain by a reflection vector polytope and robust controller design by quadratic programming approach. The roots placement of reflection vectors is studied and the weights...
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