Exploiting spectral properties of symmetric banded Toeplitz matrices, we describe simple sufficient conditions for positivity of a trigonometric polynomial formulated as linear matrix inequalities (LMI) in the coefficients. As an application of these results, we derive a hierarchy of convex LMI inner approximations (affine sections of the cone of positive definite matrices of size m) of the non...

Abstract. This paper is concerned with the exponential mean-square stabilization problem via dynamic output-feedback controller for Markovian jump systems with nonlinear perturbations and time delays which are time-varying in an interval and depend on the system mode. Sufficient delay-range-dependent stabilization conditions for the existence of robust output-feedback controller are proposed in...

This paper concerns the robust ‘practical’ stabilization for a class of linear controlled stochastic differential equations subject to both multiplicative and additive stochastic noises. Sufficient conditions of the stabilization are provided in two senses. In the first sense, it is proven that almost all trajectories of the stochastic model converge in a ‘mean-square sense’ to a bounded zone l...

Techniques for stabilization of linear descriptor systems by state-derivative feedback are proposed. The methods are based on Linear Matrix Inequalities LMIs and assume that the plant is a controllable system with poles different from zero. They can include design constraints such as: decay rate, bounds on output peak and bounds on the state-derivative feedback matrix K, and can be applied in a...

This paper deals with the control law design with an observer for models in the Takagi–Sugeno's (TS) form in the general case where the nonlinearities and the variables involved are not measurable. The proposed observer design method is based on the use of the second method of Lyapunov and the pole placement method. Based on this procedure an algorithm is proposed for stabilisation of permanent...

This paper addresses the robust H∞ issue of uncertain Markovian jump linear systems (MJLSs) with mode-dependent time-delays. A new delay-dependent condition on the stochastic stability is proposed by a new stochastic LyapunovKrasovskii functional. The stability conditions are formulated as bilinear matrix inequalities solvable by an iterative linear matrix inequality (LMI) method. Then a new ro...

In this paper, the problem of exponential stability for a class of polytopic neutral systems with nondifferentiable interval time-varying delays is studied. By using an improved Lyapunov–Krasovskii parameter-dependent functional and linear matrix inequality (LMI) technique, new delay-dependent sufficient conditions for the exponential stability of the systems are first established in terms of l...

In the last decade, the Jensen inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to derive tractable stability conditions expressed in terms linear matrix inequalities (LMI). However, it is also well-known that this inequality introduces an undesirable conservatism in the stability conditions and looking at the literature, ...

In the last decade, the Jensen’s inequality has been intensively used in the context of time-delay or sampled-data systems since it is an appropriate tool to obtain tractable stability conditions expressed in terms linear matrix inequalities (LMI). However, it is also well-known that this inequality unavoidably introduces an undesirable conservatism in the stability conditions and looking at th...

In this paper the use of Homogeneous Polynomial Lyapunov Functions (HPLFs) for robust stability analysis of linear systems subject to time-varying parametric uncertainty, affecting rationally the state transition matrix, is investigated. Sufficient conditions based on Linear Matrix Inequalities (LMI) feasibility tests are derived for the existence of HPLFs, which ensure robust stability when th...