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This paper presents new results concerning the stability analysis and design of state-feedback controllers for continuous-time Takagi–Sugeno (T–S) fuzzy systems via fuzzy Lyapunov functions. The membership functions of the T–S fuzzy systems are modeled in a space that is defined by the Cartesian product of simplexes called a multisimplex. If the time derivatives of the membership functions are bounded, the bounds are used to construct a polytope that models the space of the time derivatives of the membership functions. Linear matrix inequality (LMI) relaxations that are based on polynomial matrices are provided for stability analysis and controller design. Extensions for the design of control laws that minimize upper bounds to \\scr H2 and \\scr H\infty norms are also given. The main novelty of this method is that it allows one to synthesize control gains, which depends only on some premise variables that are selected by the designer. Numerical experiments illustrate the flexibility and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This article deals with the model predictive control (MPC) design problem for systems which are linearly dependent on a time-varying parameter. The main novelty is that, motivated by practical issues, the bounds on the rate of variation of the parameters are taken into account in the control design. Moreover, a Lyapunov function depending multiaffinely on the parameters computed at a set of instants of time and a parameter-dependent control gain are used to provide an upper bound to a quadratic performance index. The solution is obtained by means of a semidefinite programming algorithm. Examples illustrate the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

This article is concerned with robust stability of uncertain discrete-time linear systems. The matrix defining the linear system (system matrix) is assumed to depend affinely on a set of time-invariant unknown parameters lying on a known polytope. Robust stability is investigated by checking whether a certain integer power κ of the uncertain system matrix has spectral norm less than one. This peculiar stability test is shown to be equivalent to the positivity analysis of a homogeneous symmetric matrix polynomial with precisely known coefficients and degree indexed by κ. A unique feature is that no extra variables need to be added to the problems being solved. Numerical experiments reveal that the value of κ needed to test robust stability is mostly independent of the system dimension but grows sharply as the eigenvalues of the uncertain system approach the unit circle. By identifying the proposed stability test with a particular choice of a parameter-dependent Lyapunov function, extra variables can be introduced, yielding linear matrix inequalities optimisation problems of improved convergence. [ABSTRACT FROM AUTHOR]

The problems of robust stability analysis and state feedback control based on gain-scheduling for continuous-time systems with time-varying parameters that have bounded rates of variation and lie inside a polytope are addressed in this article. With respect to previous results in the literature, two main contributions of the article are: (i) the robust stability analysis conditions are less conservative and demand less computational effort than the existing ones; (ii) the conditions can be extended to cope with the problem of control design for this class of system. Parameter-dependent linear matrix inequality (LMI) conditions are given for the existence of a parameter-dependent Lyapunov function quadratic in the state and homogeneous polynomially of arbitrary degree in the parameter assuring robust stability. Two convex procedures based on LMIs exhibiting distinct complexities are proposed to solve the problem of robust stability. An extension to deal with the computation of a stabilising parameter-dependent state feedback gain for this class of time-varying systems is also provided, as a sequence of LMIs of increasing precision. Examples illustrate the results, including comparisons with other techniques from the literature. [ABSTRACT FROM AUTHOR]