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This paper proposes a method to estimate the region of attraction of nonlinear polynomial systems. Based on quadratic Lyapunov functions, stability analysis conditions in a ??quasi??-LMI form are stated in a regional (local) context. An LMI-based optimization problem is then derived for computing the Lyapunov matrix maximizing the estimate of the region of attraction of the origin.
We propose a compositional stability analysis framework for verifying properties of systems that are interconnections of multiple subsystems. The proposed method assembles stability certificates for the interconnected system based on the certificates for the input-output properties of the subsystems. The decomposition in the analysis is achieved by utilizing dual decomposition ideas from optimization...
The problem of designing H?? dynamic output-feedback controllers for polytopic Delta operator systems is considered. Given a transfer function matrix of a system with polytopic uncertainty, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states. To this model, a new polynomial parameter-dependent approach to state-feedback...
In this paper, the rank stability radius problem is proposed for a real matrix under structured scalar perturbations and some interesting results are achieved based on polynomial analysis. In addition, a computable formula and a two-step procedure are obtained which nicely solves the problem in this simple setup. Finally, these results on rank stability radius are used to estimate the stability robustness...
This paper proposes a reactive motion controller for a humanoid robot to maintain balance against a large disturbance, by relatively stepping. A reactive step is performed by the robot, so that it reduces the disturbance force. Several problems are addressed: first the motion is designed to ensure the respect of stepping constraints such as a dynamical stability, motion feasibility of the swing leg...
This paper gives a new procedure for robustness analysis of linear time-invariant (LTI) systems whose state space coefficient matrices depend polynomially on multivariate uncertain parameters. By means of dual linear matrix inequalities (LMIs) that characterize performance of certain LTI systems, we firstly reduce these analysis problems into polynomial matrix inequality (PMI) problems. However, these...
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 studies the global regulation problem for a class of nonlinear polynomial systems subject to both dynamic uncertainty and static uncertainty. The dynamic uncertainty does not vanish at the origin of the state space and thus is not input-to-state stable (ISS). As a result, the small gain theory based robust control technique alone cannot handle this problem. We manage to integrate both robust...
A novel method is proposed for the digital redesign of analogue controllers with account for the closed-loop system performance in continuous time. The method, which is based on a two-level optimization algorithm, makes it possible to place the closed-loop poles inside a specified region of the complex plane and provides for reduced-order controllers. The effectiveness of the proposed technique is...
Given a nominal plant, together with a fixed neighborhood of this plant, the problem of robust stabilization is to find a controller that stabilizes all plants in that neighborhood (in an appropriate sense). If a controller achieves this design objective, we say that it robustly stabilizes the nominal plant. In this paper we formulate the robust stabilization problem in a behavioral framework, with...
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...
This paper presents stability analysis of polynomial fuzzy control systems using sum-of-squares (SOS) approach. To take continuous form of membership functions into the stability analysis, based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived where each term contains product of polynomial fuzzy model and polynomial fuzzy controller membership functions...
This paper presents the stability analysis of polynomial fuzzy-model-based control systems, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Based on the Lyapunov stability theory, the stability analysis is generalized by bringing the membership functions as polynomial variables to the stability analysis for relaxation of SOS-based...
In this paper, we present a new approach for the stability analysis of continuous-time recurrent fuzzy systems (CTRFS). The approach is based on the representation of a CTRFS as a switched polynomial system, for which a Lyapunov function is constructed in a two step procedure. Both steps are based on semidefinite programming. The applicability is shown by an ecological system formulated as a rule...
This paper studies the stability of linear neutral delay differential systems with two delays. Based on the generalized Sturm criterion and the Sylvester resultant technique, algebraic criterion for delay-independent stability of neutral differential systems will be obtained. As an application, an example is given at last.
In this paper, we consider robust stability of interval polynomials of which stability region is the special left sector. The argument of the boundary of the special left sector is expressible as an irrational number multiplied by the circle ratio. We show that a family of interval polynomials is robustly stable if and only if a small set of vertex polynomials are robustly stable. This new result...
The paper investigates the problem of designing a digital controller with guaranteed performance for a continuous-time plant with time-delay. The proposed design technique is based on the parametric transfer function concept and numerical optimization.
This paper presents an indirect adaptive stabilization scheme for first-order continuous-time systems under saturated input which is described by a sigmoidal function. The singularities are avoided through a modification scheme for the estimated plant parameter vector so that its associated Sylvester matrix is guaranteed to be non-singular and then the estimated plant model is controllable. The modification...
Low gain feedback refers to a family of stabilizing state feedback gains that are parameterized in a scalar and go to zero as the scalar decreases to zero. Low gain feedback was initially proposed to achieve semi-global stabilization of linear systems subject to input saturation. It was then combined with high gain feedback in different ways for solving various control problems. The resulting feedback...
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...
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