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We provide an exact solution to two performance problems-one of disturbance attenuation and one of windowed variance minimization-subject to exponential stability. Considered are switched systems, whose parameters come from a finite set and switch according to a language such as that specified by an automaton. The controllers are path-dependent, having finite memory of past plant parameters and finite foreknowledge of future parameters. Exact, convex synthesis conditions for each performance problem are expressed in terms of nested linear matrix inequalities. The resulting semidefinite programming problem may be solved offline to arrive at a suitable controller. A notion of path-by-path performance is introduced for each performance problem, leading to improved system performance. Non-regular switching languages are considered and the results are extended to these languages. Two simple, physically motivated examples are given to demonstrate the application of these results.

This paper considers asymptotic stability and transient performance of discrete-time piecewise affine systems. We propose a procedure to construct a nested sequence of finite-state symbolic models, each of which abstracts the original piecewise affine system and leads to linear matrix inequalities for guaranteed stability and performance levels. This sequence is in the order of decreasing conservatism, and hence gives us the option to pay more computational cost and analyze a finer symbolic model within the sequence in return for less conservative results. Moreover, in the special case where this sequence is finite, an exact analysis of stability and performance is achieved via semidefinite programming.

The problem of jointly synthesizing a supervisor, a measurement scheduler, and a feedback controller for discrete-time linear systems is considered. It is shown that open-loop supervisory and scheduling laws are nonconservative for robust exponential stability and H2 and H∞ type performance requirements, and that they can be obtained separately from the feedback controller. All the design conditions are formulated in terms of linear matrix inequalities.

Decentralized sequential detection problems with communicating detectors are solved under the assumptions that the observations are independent and uniformly distributed and that decision errors are uniformly penalized. For the cases of one-step delayed, sequential, and nonsequential signaling, explicit decision rules are proposed and exact conditions for their member-by-member optimality are derived. These decision rules approximate high-performance threshold rules with very strict thresholds when decision errors are heavily penalized.

Given a multi-modal linear plant, the objective is to obtain a mode switching sequence and a switching-path-dependent feedback controller that jointly stabilize the plant and achieve a desired LQG performance. The synthesis of a dynamic output feedback controller can be carried out separately from that of a switching sequence between modes. Moreover, the switching sequence can be obtained by iteratively solving convex programs.

For discrete-time switched linear systems under nondeterministic autonomous switching, the existence of causal finite-path-dependent stabilizing output injection and state feedback laws are characterized by increasing unions of linear matrix inequality conditions. These convex characterizations lead to the notions of causal finite-path-dependent detectability and stabilizability, which in turn yield a separation result for dynamic output feedback stabilization. By generalizing the standard duality concept to switched systems under arbitrary switching path constraints, we relate these notions to direct extensions of time-varying detectability and stabilizability requirements.

Well-known properties of uniform detectability and uniform stabilizability are sharpened in terms of Lyapunov and Riccati inequalities for discrete-time linear time-varying systems. In particular, it is shown that the stabilizing output injection law can be taken to depend solely on a finite path of past and present system coefficients and the stabilizing state feedback law solely on a finite-path of present and future coefficients. These results are applied to time-varying systems where the system coefficients vary among a finite set, and lead to precise and computable convex conditions for the stability and dynamic-output-feedback stabilizability of such systems.

We are concerned with the output norm-constrained infinite-horizon linear quadratic regulation problem, where the underlying state-control constraints are specified by curved, rather than polyhedral, surfaces. Each suboptimal problem admits an exact convex synthesis condition expressed by an increasing union of linear matrix inequalities and results in an eventually time-invariant controller satisfying the desired performance level subject to given constraints and closed-loop stability. The output norm-constrained minimum-time control problem is also dealt with as a corollary.

A set of switching sequences of a discrete-time switched linear system is said to be uniformly stabilizing if the system is uniformly exponentially stable over all switching sequences that belong to the set. Based on the recent result that a switched linear system is uniformly stable if and only if an increasing countable union of linear matrix inequality conditions is satisfied, we characterize all uniformly stabilizing sets of switching sequences. A discrete-time hybrid automaton of the automobile engine is considered to illustrate the result

For discrete-time polytopic linear parameter-varying systems, the uniform exponential stability, which is equivalent to the asymptotic stability and includes the quadratic stability as a special case, is characterized by the union of an increasing family of linear matrix inequality conditions. On the other hand, in certain cases, nonconservative synthesis of uniformly stabilizing controllers is achieved via a system of finite number of linear matrix inequalities if the controller is allowed to have finite memory of past parameters. Two such cases are robust state feedback (in a relaxed sense) against polytopic parameter variations, and multiple output injections under polytopic fusion rules