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A systematic stabilization approach is provided for systems whose regulation error dynamics is subject to rational nonlinearities given prior knowledge of the system zero-error steady-state condition and a proper internal model. The error dynamics is cast in a differential-algebraic form so as to address the synthesis of controller parameters by a numerical optimization problem subject to bilinear matrix inequality constraints. A particular case is also explored where the resulting constraints are linear matrix inequalities.

International audience; This paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time-varying input delay and polytopic parameter uncertainty. A linear matrix inequality approach based on the Lyapunov-Krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction. Two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states. Numerical examples demonstrate the potentials of the proposed stabilization approach.

Although there has been a lot of research on analysis and synthesis of quantized feedback control systems, most results are developed for the case of a single quantizer (either measurement quantization or control signal quantization). In this technical note, we investigate the case of feedback control systems subject to both input and output quantization. This is motivated by the fact that it is common in remotely controlled systems that measurement and control signals are shared over a single digital network. More specifically, we consider a single-input single-output linear system with memoryless logarithmic quantizers. We firstly show that the output feedback quadratic stabilization problem in this setting can be addressed with no conservatism by means of a sector bound approach. Secondly, we provide a sufficient condition for quadratic stabilization via the solution of a scaled H? control problem. Finally, we analyze a problem of bandwidth allocation in the communication channel for finite-level input and output quantizers.

This technical note develops a robust stability analysis method for a class of implicit polynomial systems subject to uncertain constant parameters. A polynomial (with respect to the state and uncertain parameters) Lyapunov function is computed to assess the robust local stability of the system and to provide a robust estimate of the domain of attraction. The results are given in terms of linear matrix inequalities that are affinely dependent on the system state and uncertain parameters. Numerical examples illustrate the effectiveness of the developed approach.

This note addresses the problem of robust stability analysis for a class of Markov jump nonlinear systems subject to polytopic-type parameter uncertainty. A condition for robust local exponential mean square stability in terms of linear matrix inequalities is developed. An estimate of a robust domain of attraction of the origin is also provided. The approach is based on a stochastic Lyapunov function with polynomial dependence on the system state and uncertain parameters. A numerical example illustrates the proposed result

In this note, we present corrections to our previous paper "Switching rule design for switched dynamic systems with affine vector fields" [1], [2]. The correction is necessary to guarantee the stability of the system under sliding motion, which is not ensured from [1], [2] due to an error in the expressions (11) of the original paper [1]. To correct the results it is necessary to add a new condition to the results of [1], [2]. If there is no sliding motion or if the sliding motion dynamics, in the sense of Filippov, satisfies a quadratic stability condition, the additional condition is not necessary. The corrections in this note are restricted to the case of two operation modes.

In this paper, we consider the problem of guaranteed cost control for a class of uncertain nonlinear systems. We derive linear matrix inequality conditions for the regional robust stability and performance problems based on Lyapunov functions which are polynomial functions of the state and uncertain parameters. The performance index is calculated over a set of initial conditions. Also, we discuss the synthesis problem for a class of affine control systems. Numerical examples illustrate our method.